I 



i 



J^u.^J /<A. 72/. 



ARTIS LOGICiE 



RUDIMENTA. 



ARTIS LOGICiE 



RUDIMENTA, 



FROM 



Vl 



THE TEXT OF ALDRICH, 



WITH NOTES AND MARGINAL REFERENCES. 



REV. H. L. -MANSEL, B.D. 

TUTOR AND LATE FELLOW OF ST. JOHN'S COLLEGE, AND READER IN 
MORAL PHILOSOPHY, MAGDALEN COLLEGE. 



THIRD EDITION, CORRECTED AND ENLARGED. 



OXFORD, 

WILLIAM GRAHAM : 

WHITTAKER AND CO. LONDON. 

1856. 

I- 



^oi> 






28957 




BAXTER, PRINTER, OXFORD. 



PREFACE. 



Whatever variety of opinion may exist as to 
the absolute merits of Aldrich's Logic, there are 
many considerations which recommend a new 
edition of that work, as by far the most convenient 
mode of supplying an acknowledged deficiency in 
the studies of the University. The majority of 
Teachers will probably agree with me in regarding 
the dry skeleton of a Latin Manual as better 
adapted to the discipline of beginners than any of 
the more elegant, but somewhat diluted Essays of 
the present day : to which must be added the 
consideration, that Latin is the original language 
of many of the technicalities of the subject, which 
cannot be so conveniently learned through the 
medium of a translation. But among the Latin 
Compendia, that of Aldrich has long reigned 
almost exclusively in Oxford ; nor would it be 
easy to select any rival manual of such decided 
superiority as to counterbalance the evils neces- 
sarily attendant on all violent changes in a long- 
established system. Deficient as the work unde- 

b 



VI PREFACE. 

niably is in many of the prominent features of the 
Scholastic Logic, its very deficiencies render it in 
some respects preferable to a more faithful expo- 
nent. The criticism of the present age has con- 
tributed much towards a more just appreciation of 
the merits of the mediaeval Philosophy ; but he 
must be a bold champion of reaction who would 
advocate the complete disinterment of the Logic 
of the Schools. Who would desire now to oppress 
the Student with the heavy burden of modals, or 
to bewilder him with the mysteries of Suppositio, 
Ampliatio, Restriction and the whole farrago of the 
Parva Logicalia? Omissions of this character 
may, with equal probability and more charity, be 
attributed to the sound judgment of the University, 
than to the decline of the Professorial System and 
the incompetency of College Tutors % 

On the other hand, it must be confessed that 
there is much to be added to this or any other 
Compendium, to enable it to meet the demands of 
the existing University Examinations. This will 
at once be admitted by all who have had any 
recent practice in tuition ; it may be easily ascer- 
tained by any who will take the trouble of com- 
paring the contents of the book with those of 
any of the present examination-papers. To this 
deficiency, the increasing study of the original 
writings of Aristotle has not a little contributed. 
But the transition from the bare text of Aldrich to 
^ See Edinburgh Keview, No. 115. p. 195. 



PREFACE. Vll 

that of Aristotle is far too abrupt to be beneficial 
to the Student. Occasionally indeed he may 
recognise an old friend in a new dress ; but the 
difference of language, order, and manner of 
treatment will conceal from the unpractised eye 
most of the passages in which his Latin successors 
have attempted any thing more than a bare 
translation of the words of the Stagirite. 

In this respect, it is hoped that the numerous 
references to, and quotations from, the Oiganon, 
which will be found in the following pages, will 
contribute in some degree towards a most important 
object, — the clear discrimination between those 
portions of the system w^iich belong to the original 
work of Aristotle, and those for which we are 
indebted to subsequent Logicians. For a like rea- 
son, in my references to the latter, I have occa- 
sionally endeavoured to furnish some information 
as to the author and the period of the innovation. 
Nothing is more strongly to be reprehended than the 
slovenly practice of referring in general terms to 
the Logic of the Schoolmen ; as if every individual 
of that body had written a distinct treatise on the 
subject, or as if those who have were a race of 
harmonious commentators, whose labours exhibit a 
supernatural uniformity, such as tradition narrates 
of the translators of the Septuagint. What would 
be thought of a reference in general terms to the 
doctrine of the Greek Philosophers ? Yet Aristotle 
scarcely departed more widely from Plato, than 

b2 



Vm PREFACE. 

did Abelard from William of Champeaux, or 
Occam from Scotus. In some cases it is indis- 
pensable to the right understanding of doctrines 
and modes of expression, to know when and by 
whom they were first introduced into Logic. If, 
for example, as in the treatment of the Predicables 
and of Definition, we find language held neither by 
Aristotle nor by Porphyry, expressly insisted on 
by one sect of the Schoolmen, and as expressly 
repudiated by another, there can be no doubt 
what views, whether right or wrong in themselves, 
must be adopted as a necessary basis for the inter- 
pretation of that language. 

Of my own very imperfect acquaintance with the 
post-Aristotelian Logicians, I am well aware. But 
when the alternative lies between the postponement 
of the present work to an almost indefinite period, 
and the attempting it from such resources as I can 
at present command, the necessity that has long 
been felt for something of the kind, will, I trust, 
be allowed as some apology for the deficiencies of 
the execution. 

One other point remains to be noticed. In com- 
menting, whether for explanation or correction, on 
the language of a manual so brief as that of Aldrich, 
there is no tutor but must have felt the difiiculty 
of attaining the happy medium between dogmatic 
assumption on the one hand and prohx discussion 
on the other. It is possible so to bewilder a pupil 
with premises that he shall utterly lose sight of the 



PREFACE. IX 

conclusion : it is possible so to overwhelm him with 
assertion^ as to leave him no choice but th^t of 
blind submission to the ipse dixit of his tutor or 
the ipse scripsit of his text-book. The same 
difficulty meets the editor. In controverting 
the positions of a work which for more than a 
century and a half has enjoyed the sanction of 
the University, somewhat more of the verecunde 
dissentio is becoming than can always be comprised 
within the necessary limits of a foot-note. The 
further discussion of such points in an Appendix 
has in some instances unavoidably produced a 
certain amount of repetition. This however, though 
injurious to the form of the work, will, it is hoped, 
not render it the less serviceable to that not in- 
considerable class of students 

oig ouls 7 gig XsyovTsg l^ixvo6[ji.sQot. 

A few passages omitted in recent editions of the 
Compendium have been restored in the present. 
This, however, has been done but sparingly. An 
account of the Arbor Porphyriana has been trans- 
ferred to the first chapter from its original place in 
the Penus Logica, The obvious utility of the 
insertion will, it is hoped, warrant the liberty in 
this single instance taken with the text. 

The references to Aristotle have been adapted 
to the Oxford reprint of Bekker's text. In 
Germany, a custom seems to be gaining ground 
of referring to the pages of the Berlin edition, 
but that work has not been sufficiently circulated 



X PREFACE. 

here to make the example convenient to follow. 
Of the Isagoge of Porphyry, Buhle's edition has 
been used. With the Greek Commentators, my 
chief acquaintance has been made through the 
medium of the Berlin Scholia collected by Brandis, 
to which, as the most accessible edition, reference 
has been made. Boethius is quoted from the 
Basel edition of 1570. The other quotations will 
in most instances speak for themselves. 

To the present edition is prefixed an Intro- 
duction, containing a short historical account of 
logical writers^ ancient and modern, which, though 
necessarily cursory and incomplete, will, it is hoped, 
be found more satisfactory than the notices which 
can be gathered from most English works of a 
similar character. In this sketch I have derived 
considerable assistance from the valuable Essay of 
M. St. Hilaire. Mr. Blakey's elaborate History of 
Logic has been occasionally consulted ; but his 
principle of classification and examination is too 
different from mine to enable me to make much 
use of his labours. My critical views of Logic are 
briefly exhibited in the second part of the Intro- 
duction, and have been pubhshed at greater length 
in a separate work. Some apology is perhaps 
needed for the references to this work which will 
be found in the following pages, especially in the 
earlier portion. But I have long been of opinion 
that Logic, as generally taught, requires constant 
illustration from Pyschology, and that the earlier 



PREFACE. XI 

part of Aldrich's text in particular is especially 
liable to be misunderstood without some such 
assistance as it was one principal aim of the 
Prolegomena Logica to supply. My obligations 
in the present work, as in that, to the writings of 
Kant, of M. Cousin, and of Sir William Hamilton, 
require special acknowledgment; to these works 
must be added here the logical works of Professor 
Trendelenburg, Waitz's excellent edition of the 
Organon, and Biese's " Philosophic des Aristo- 
teles/' 



INTRODUCTION. 



PART I. HISTORICAL. 

Although the writings of Aristotle are the source from History of 
which the science of Logic is principally derived, it is Logic 
remarkable that there is no single name sanctioned by 
the Stagirite himself, under which can be comprehended 
either the whole collection of treatises known by the 
name of the Organon, or the whole subject of which they 
treat. Aoyix^, as the name of an art or science, is not to 
be found in his works, and the cognate terms, Xoyixos and 
KoyiKoog, are used in a very different sense from that 
which has subsequently been given to them^ The J"/^ zl^-'^-^ 
logical syllogism of Aristotle is opposed sometimes to the 
analytical, sometimes to the physical, sometimes to the 
demonstrative syllogism ; and signifies a ])rocess of 
reasoning from general principles of probability, as 
distinguished from one of which the principles are 
elicited by special contemplation of a given object or 
notion ^\ It is therefore opposed, alike to the demon- 
strative reasoning, in which necessary truths are resolved 
into the axiomatic principles on which they depend, 
and to that by which physical phenomena are referred 
to general laws of nature. 

The first use of the term Logic, as the name of a 
science, is probably later than Aristotle, and to be re- 

=^ Cf. Anal. Post. i. 22. 10. i. 24. 11. ii. 8. 3. Top. i. 14. 1. Phi/s. iii. 3. 2. 

^ See Gassendi, Logicce Proccvunm xn'it. Biese, Philosophie dcs Arislotelcs, 
vol. i. p. 133. Waitz, Organon, vol. ii. p. 353. Trendelenburg, Elimcnia, 
p. 47. 



XIV INTRODUCTION. 

ferred to Zeiio the Stoic. The division of Philosophy 
into Logic, Physics, and Ethics, probably originated 
with this Philosopher^ and the use of the name Logic in 
Cicero is principally in relation to the Stoical doctrines'^. 
For the application of the term to the contents of the 
Aristotelian Organon, the Greek commentators upon 
Aristotle are our earliest extant authority. Alexander 
of Aphrodisias, the oldest of these whose works have 
come down to us% speaks of ^ Xoyix^ xai a-uWoyia-TiJcvj 
TrgotyfLocTelu as containing under it aToSejxrixi^, SiaAsxriJc^, 
TTsigota-TixYji and (j-o(Pk7tikv) ^ Here, while Dialectic retains 
its Aristotelian sense. Logic is extended so as to include 
the syllogistic theory in general, and its particular appli- 
cations to necessary and probable matter. A similar 
extension of Dialectic is found in the commentaries of 
David the Armenian s; and Philoponus uses both terms 
as synonymous, and in the same extent^. 

<= Laert. vii. 39. Plutarch, De Plac. Phil. i. 1. This division is some- 
times attributed to Plato. (Cf. Cicero, Quasi. Acad. i. 19. De Fin. i. 22. 
Euseb. PrcBp.Evan.-sx. 1. Augustin, De Civ. Dei, viii.4.) But none of the 
three names occur in any of the extant Platonic writings ; and a different 
division of sciences into cognitive and practical is intimated by Plato 
himself, Polit. p. 258. Indeed the state of philosophy in Plato's day 
would hardly allow of the Stoical division being made. Cf. Van Heusde, 
Initia Phil. Platon. p. 41. 117. Aristotle's supposed adoption of the same 
threefold classification is still more questionable ; being founded on a 
misinterpretation of Topics, i. 14. 4. and at variance, as well with the 
earliest commentary on that passage, as with Aristotle's constant use of 
the word KojikSs, and with his Avell-known division of theoretical Philo- 
sophy into Physics, Mathematics, and Theology. 

^ Tusc. Qucest. iv. 33. Cf. Trendelenburg, Elementa, p. 47. 

e The Paraphrase on the Ethics, attributed to his predecessor Andronicus 
Rhodius, is spmious. Its real author is probably HeUodorus Prusensis. 
See Sainte-Croix, Examen Critique des Anciens Histoires d' Alexandre le 
Grand, p. 524. 

f Scholia, p. 141. a. 19. The testimony of Boethius {In Top. Cic. p. 766.) 
would seem to refer this usage of the word to the elder Peripatetics, but 
we must reject hit? reference to Aristotle. 

? Scholia, p. 18. a. 34. Waitz, vol. ii. p. 437. 

h Scholia,^, 143. a. 4. 



INTRODUCTION. XV 

Two names sanctioned by Aristotle are applicable to Names 
parts, but to parts only, of the Organon. These are Aristotle. 
Analytic and Dialectic. The former term is applied by Analytic. 
Aristotle to the four books which treat of the syllogism 
and of demonstration^, and appears to denote the reso- 
lution of the reasoning process into its scientific forms. 
This w^ord is the most nearly synonymous with the 
modern Logic of any used by Aristotle himself; but it 
embraces the process of Reasoning. only, to the exclusion 
of Conception^and Judgment^. Dialectic is a word pro- Dialectic, 
bably invented by Plato ^, though afterwards applied to 
the works of earlier philosophers, e.g. Zeno the Eleatic. 
In its Platonic sense it denoted the highest of all 
sciences ; that which takes cognisance of the eternal 
and immutable, of being in general and its attributes, 
and thus has insight into the universal principles upon 
which all other knowledge is dependent". It thus 
corresponds in matter, though different in form, with 
the first Philosophy or Theology of Aristotle, afterwards 
called Metaphysics. The name Dialectic had reference 

• Galen {de libris propriis, ch. II.) says that the title Analytica is not 
Aiistotelian ; the Prior Analytics being called by their author ircpi avWo- 
yia-fiov, and the Posterior, Trept airoSel^ecos. This testimony is accepted by 
M. St. Hilaire, Memoire. p. 42. But the name ayaXvriKct occurs too 
frequently in Aristotle's own writings to warrant this view, unless we 
suppose (which is very improbable) that all the references have been 
interpolated by a later hand. Cf. Waitz, vol. i. p. 367. The distinction, 
however, between Prior and Posterior Analytics is not recognised by 
Aristotle, and we may perhaps conjecture that the name avaXvTiKo. was 
given by him to the entire four books, each dirision being also distin- 
guished by its own title, as mentioned by Galen. 

^ Q>i. An. Pr. i. 33. 2. Toi/s yeyii/rjfxevovs avWoyidfiovs ayoAvoi/xey eis ra 
wpoiipTjfjLeua o-x^Maro. Cf. Trendelenburg, Elementa, p. 47. Waitz, vol. i. 
p. 36b. The analytical method of inquiry, attributed to Plato by Laertius, 
iii. 24.is his method of division, exemplified especially in the Sophistes and 
Politicus; though he does not give it the name of analysis. 

1 See PhcBdrus, p. 266. Laert. iii. 24. Cousin's Plato, vol. vi. p. 450. 

"> Phcedrus, p. 276. SojMst. p. 253. Repitb. vi. p. 510 sqq. vii. p. 021. 534. 
Cf. Van Heusde, Initio, p. 247. 



XVI INTRODUCTION. 

to the colloquial form, which, whether in solitary medi- 
tation, or in conversation with others, Plato regarded as 
the true method of eliciting and communicating know- 
ledge"; a view intimately connected with his doctrine 
of ideas, and with the theory which placed all knowledge 
in reminiscence. The Dialectic of Aristotle holds a far 
lower position, being merely the act^^of ^disputing by;. 
question; of attacking and defending a given thesis, 
from principles of mere probability, such as the opinions 
of men in general, or of the majority, or of certain 
eminent authorities. The Dialectical Syllogism is thus 
the same as the Logical; and the names Logic and 
Dialectic, if used solely in conformity with Aristotle's 
authority, would correspond, not to the Organon as a 
whole, but only to the two last treatises, the Topics and 
Sophistic Refutation s°. 
Hisory of Thus much may suffice, as regards the origin and use 
Science. ^^ ^^^ name Logic and the cognate terais. More im- 
portant is the inquiry, to w^hat extent the science itself, 
as exhibited in Aristotle, is indebted to the labours of 
previous philosophers. Dialectic, the thing though pro- 
bably not the name, is regarded, on the authority of 
Zeno the Aristotle, as the invention of Zeno the Eleatic^. By this 
is probably only meant that Zeno was the first to employe 
dialogue as the medium of philosophical instruction ; 
his predecessors of the same school, Xenophanes and 
Parmenides, having communicated their doctrines in 
verse. The dialectic method was afterwards exten- 
sively used by different schools, and for different pur- 
poses, which ultimately obtained distinctive names. 

n ThecEt. p. 189. Soph. p. 2C3. Phcedrus, p. 275. Protag. p. 329. 

o Top. i. 1. 2. 

P Laert. ix. 25. But in another passage (iii. 48.) he quotes Aristotle, 
as attributing the first written dialogues to Alexamenus of Styra. See 
Athenaeus, xi. 102. 



Eleatic. 



INTRODUCTION. XVll 

Aristotle enumerates four different kinds of reasoning, 
to which the colloquial form (to ^laXsysa-Qon) was applied, 
\6yoi StSacrxaXixo/, dioiXsKTixol, TtsipaarriKol, and spKyTixoii. 
The first are demonstrative reasonings, from the proper 
and axiomatic principles of a given subject. The second, 
or dialectic reasonings in the Aristotelian sense of the 
term, are those derived from general principles of proba- 
bility, such as the opinions of the majority of mankind, 
or of philosophers. The third are only a special appli- 
cation of probable reasonings to expose the ignorance , 
of pretenders in science '". The fourth are fallacious 
reasonings, from apparent but not real probabilities. In 
a subsequent passage, he distinguishes between egiariKol 
and jo^jiCTTixo/ ; the former being such as employ fallacy 
merely for a display of skill ; the latter, for pecuniary 
profit. Hence he defines (ro^Krrixr) as x^rii/.ccTKrTix.Y} tic, Sctto 
(ro(plu5 (pctivo[ji.svYi^\ These distinctions however will be of 
comparatively late origin ; after the various applications 
of the original method of Zeno had rendered specific 
names necessary. 

The eristic or sophistic was, as might naturally be The So- 
expected, the earliest of these special developments of 
the dialectic method. The arguments of Zeno himself 
had no small affinity to sophistry ; and the state of 
philosophy at that period was such as naturally to 
promote further advance in the same direction. The 
conflicting opinions of the three great pre-Socratic 
schools, the Ionian, the Pythagorean, and the Eleatic ; 
the one-sided and exclusive character of their principles, 



q Soph. Elench. 2. 1. 

>■ Kritik des dialektischcn Scheins, Kant, Kritik der r. V. p. G4. Kant is 
unjust to the ancient dialectic, when he describes it as a sophistical art of 
giving illusion the appearance of truth. The tentative use of dialectic very 
nearly corresponded with his own. 

=• Soph. Elench. It. 1, 5. 



XVlll INTRODUCTION. 

combined with the universality of their aims, and the 
consequent failure of each in the attempt to resolve diffi- 
culties beyond their respective provinces — all this could 
hardly fail to produce a spirit of scepticism, which should 
end in denying the possibility of attaining to truth at 
all*. Such w^as the purpose of the eristic method of the 
Sophists. They employed it chiefly to enforce their 
leading dogma of the unreality of all knowledge, specu- 
lative or practical. Accordingly, they endeavoured, by 
ingenious applications of the dialectic mode of reasoning, 
to involve those with whom they disputed in self-con- 
tradictions and absurdities ; and thus to shew that, what- 
ever principles we start from, paradox and inconsistency 
will be the invariable result. At a later period, the 
eristic method was adopted and pursued to a consider- 
able extent by Euclid of Megara, and his successors 
Eubulides, Diodorus Cronus, Alexinus, and Stilpo. 
Socrates. On the other hand, the method of Socrates partook 
largely of the Trsj^ao-rtjcrj, or tentative, which Aristotle 
describes as follows, r} yag Trsigaa-TiKY) ka-n SiaXsjcTtxij ri§ koc) 
$scogel ou rov slhoTu ocWoi rov uyvoomru xolI '7rgo<r7roio6ixsvov. 
The opinion which Socrates entertained of the pro- 
fessions of his contemporaries, and his manner of 
exposing their ignorance, appears in his well-known 
explanation of the oracle which pronounced him the 
wisest of men"^; and the same conviction and exposure 
of ignorance and pretension constantly appear in the 
Platonic dialogues, as well as in the Memorabilia of 
Xenophon\ For this purpose, he insists on the superior 
fitness of his own brief discourses to the longer mode of 
reasoning employed by some of the Sophists, and says 
that many orators can discourse ably at length, but that, 

t See Plato, T^e^^. p. 152. Cra^yZ, p. 386.402. Van Heusde, Jm7m,p.l2l. 

" Plato, Apol. p. 21. 

^ Cf, Plato, Sophist, p. 230. Xenoph. Mem. iii. 6. §. 2—6. 



INTRODUCTION. XIX 

if examined by searching questions, they are like written 
books, unable to reply y. In the same spirit, like Des- 
cartes in modern times, he urges the necessity of a 
purification of the mind from prejudice and false opinions, 
as a necessary preliminary to the investigation of truth -^ 
the principal means of purification being Dialectic''. 

In all this, as well as in the Dialectic of Plato, we find 
no anticipation of any important part of the Aristo- 
telian Analytic ; though the various modifications of the 
dialectic form may have contributed more or less to that 
systematized method of disputation exhibited in the 
two last treatises of the Organon. The antecedents of 
Aristotle's more strictly logical labours appear in other 
and more subordinate points of the philosophy of his 
predecessors. We may pass over, as unquestionably 
forgeries of a later period, the Categories attributed to 
Archytas, and the other logical relics of the Pythagorean 
school*. There remain two important logical dis- 
coveries attributed by Aristotle to Socrates, Induction 
and Definition''. The Induction, however, of Socrates Socratic 
is not, like that of Aristotle, a strictly formal process 
of reasoning from the aggregate of particulars to the 
universal constituted by them. It rather resembles the 
Aristotelian Example or Parable'^, being a material 
inference from a selected number of similar or analogous 
cases to another individual instance under discussion. 
As a specimen, may be taken the following argument 
from the Gorgias. !^X2. T/ ouv ; 6 ra rex.Tovtxoi iJiSfji,ocSY,Kooc 

TSXTOVlX.Og, Yj OU ; rOP. Na/. ItI2. OvKOUT/ Ko) TU fXOVCiXCi 



y Phcedriis, p. 275. Protag. p. 329, 

^ Theat. p. 150. Cf. Sophist, p. 230. where the Socratic metliod is '^ 
described, though Socrates is not the speaker. 

" See Hamilton's Reid, p. 686. 

** Metaph. xii. 4, 5. Avo yap iariv a tis hu anoSolr} ^ujKp dTei St/cawy. jtflu*- 
r' iiraKTiKovs X6yovs koI zh-Pfii^l^^ii Ka66\ov. 

c Arist. Ehet. ii. 20. 4. TlapafioKi) Sh ra 'S.wKpariKi. 



XX INTRODUCTION. 

lxou<7ix6g ; FOP. Na*. 212. Ka» 6 T«5t \otTgi)cd largiKog ; xa) 

ToiXXa. ovTM xotToi Tov avTOv Aoyov' 6 /jtsjxaSrjxoJf sxacrra TOiouTog 

lo"T<v oiov y; l7rKrTYjU,Y] sxci(TTOv ccTTSPya^eTon ; FOP. Tltxvu ys. 

2-12. Ouxouv xara toutov tov \6yov Kot) 6 roc dUunx [j^si/,a$Yi>iCJog 

dlxonog; FOP. Uavroog S^ttou'^. A reasoning of this kind 

has no place in a system of Formal Logic. That 

science recognises no inference that is not necessitated 

by the laws of thought; whereas in instances like the 

above, it is obvious that the premises may be true, and 

yet the conclusion false ^. Or two specimens may be 

found, both complying with the above form, one of 

which shall carry conviction to every reasonable man, 

while the other is utterly worthless. Its moral force 

may thus vary " from the highest moral certainty to the 

very lowest presumption*"." Its logical value is zero. 

Socratic Xhe Definition of Socrates has also more of a material 
Definition. 

than a logical character. He continually distinguishes 

between the essence and the qualities of a thing, and 

insists on determining what a thing is, rather than what 

it resembles^ ; a distinction afterwards repudiated by his 

disciple Antisthenes, w^ho denied the possibility of real 

definition. But Definition, as treated by Socrates, is a 

contribution, not to Logic, but to Metaphysics. It does 

not analyse by the laws of pure thought the contents of 

a given notion ; but endeavours to penetrate the real 

essence of things^. The same may in some degree be 

said of the Aristotelian treatment of Definition in the 

Posterior Analytics. 

^ Gorgias, p. 460. 

e Of which the above example is adduced as a specimen by Boethius, 
Opera, p. 600. 

f Butler, Introduction to Analogy. 

g Cf. Goryias, p. 448. ThecBt. p, 146. 

^ Cf. Fries, System der Logik, §. 3. For specimens of the Socratic 
Definition and the Dialectic Method, see the inquiries into the nature of 
piety, justice, msdom, &c. Xen. Mem. iv. 6.; of holiness, Plato, Euthy- 
phron, p. 6. ; of virtue, Meno, p. 72. 



INTRODUCTION. XXI 

From the position constantly assigned to Socrates in Plato. 
be Platonic Dialogues, it is impossible to determine 
"rith any accuracy how much of the doctrines and 
nethods advocated in those writings is due to the master, 
md how much has been added by his disciple. From j 
he express testimony of Aristotle, however, we may 
!onclude that Socrates did not, like Plato, maintain the 
xistence of ideas separate from the sensible phenomena , 
)f the world^; and consequently, that the exaltation of 
dialectic from its tentative use to the rank of the science 
)f absolute being, a view intimately connected with the 
deal theory, is due to Plato rather than to Socrates. To 
lato also probably belong in a great degree the methods 
)f (Tuvaywy^ and 5ia/^eo-ij, mentioned in the Phaedrus as the 
wo principal parts of Dialectic, and illustrated at some 
ength in the Sophistes and the Politicus''. The former 
onsists in the collection of a number of scattered 
bjects, in reference to one idea, with a view to definition; 
he latter in a gradual dichotomy, by means of contrary 
r contradictory members, so as to ascertain as accurately 
s possible the number of subordinate species contained 
nder each genus. It is the careful performance of this 
rocess, proceeding gradually through the intermediate 
lasses to the lowest, that especially distinguishes the 
rue dialectic method from the eristic ^ These pro- 
esses, for which Plato was perhaps in some degree in- 
ebted to the Eleatic and Megaric Philosophy "', may be 

Metaph. xii, 4. 5. 'AAA.' 6 jxkv '2,uiKp6.rT]S to kuOSaov ov x^picrra iirolei ou5e 
ovs Spifffiovs' 01 S' 6x<^P'^<^''> '^^■^ '''^ TOiavra rwv ovtuu iScas ■trpocrrjydpeva'au, 

" Phcedrus, p. 205. 277. Soph. p. 218. Polit. p. 2G2. Phileb. p. 16. 

' Phileb. p. ] 7. With this may be compared Bacon's aphorism on the 
nportancG of axiomata media. Nov. Org. 1. i. aph. 19. Bacon indeed, 
iph. 105.) intimates that his own method was perhaps anticipated by 
lato, and this hint has been developed at greater length by Coleridge 
1 his Treatise on Method. But the accuracy of the parallel may be 
uestioned. 

Cf. Stallbaum, Prolegomena in Philebum, p. 16. 



XXll INTRODUCTION. 

regarded as the precursors of the Aristotelian doctrine 
of searching for definitions by the two opposite methods, 
afterwards known as those of Division and Induction^. 
j In Plato we find also the analysis of the Proposition, 
with the noun and the verb as its constituent elements ; 
the union of the two being necessary to every assertion. 
Aiavoia and >^oyog correspond to each other as the 6 s<rM 
and 6 s^m Xoyog of Aristotle ; the former being internal 
discourse without speech, the latter external, by the 
voice. Aoyog is divided into (Pucris and ot'7ro(poi(ris°. In this 
passage, Plato has furnished the groundwork of the 
grammatical researches of the De Interpretatione. 

The three highest laws of thought, the Principles of 
Identity, Contradiction, and Excluded Middle, are also 
indicated, though not explicitly enunciated, in Plato p. 
But neither he nor Aristotle has accurately distinguished 
between their very different positions in Logic and in 
Metaphysics. Indeed, this distinction cannot be con- 
sidered as having been made with exactness by any 
philosopher before Kant. 
Aristotle. Some few elements of the Logic of Aristotle thus 
appear in the philosophy of his predecessors ; though 
the science was not accurately distinguished either fi-om 
Grammar or from Metaphysics. A distinct treatment of 
logical questions was undeniably first undertaken by the 
Stagirite ; though still, if we regard the Organon as a 
single work, with a considerable admixture of extraneous 



" See Anal. Post. ii. 13. and Appendix, note C. 

o Sophist, p. 262. 

p The Principle of Identity may be gathered from the Sophists, p. 254 
those of Contradiction and Excluded Middle, from the Republic, iv. 
p. 436. the Phcedo, p. 103. and the Sophistes, p. 252. 250. The two latter 
principles also appear in the Second Alcibiades, p. 139 ; but this dialogue 
is generally allowed to be spurious. Aiistotle enunciates them more 
distinctly, Anal. Fr. ii. 2. Anal. Post. i. 11. i. 2. ii. 13. Metaph. iii. 3. x. 5. 
iii. 7. ix. 4. 



INTRODUCTION. XXlll 

matters, which a more accurate classification of the 
sciences would relegate to Metaphysics, to Psychology, 
to Rhetoric, or to Grammar. But Aristotle must not be 
considered as responsible for the present composition of 
the Organon, but only for six distinct treatises, which 
his commentators have combined into one volume **. Of 
these, the latter part of the De Jnterpretatione and the 
Prior Analytics may be regarded as containing most of 
the essential parts of pure Logic ; though, as regards the 
laws and forms of judgment in some degree, and of 
conception almost entirely, much must be added and 
much retrenched, before we can bring the entire pro- 
ducts of pure thought into harmony with the elaborate 
development of the various forms of the syllogism. The 
treatise on the Categories, with the early part of the De 
Jnterpretatione, is grammatical rather than logical, with 
a few trespasses on the domain of Metaphysics ; while 
the Posterior Analytics, together with the Topics and 
Sophistic Refutations, contain applications of Logic to 
necessary and contingent matter in demonstration and 
dialectic disputation, and should be accurately classed 
rather as parts of the Logica utens than of the Logica 
docens. But we are not justified in criticising the Organon 
of Aristotle as though it were a single work composed on 
a single subject. 

Of the post- Aristotelian Logicians, my limits will only Theo- 
allow a very brief notice. To Theophrastus is attributed and^Eu-^ 
the invention of the Hypothetical Syllogism, which was ^emus. 
afterwards more fully developed by Eudemus and the 
Stoics. The Stoics have already been noticed as the The Stoics, 
probable authors of the name Logic, and of the division 

*i On the composition of the Organon, some further remarks will be 
found, Prolegomena Logica, p. 261. The name Organon, according to M. 
St. Hilaire, was not habitually given to the collected works before the 
15th century. Memoire, vol. i. p. 19. 

c 2 



XXIV INTRODUCTION. 

of philosophy into Logic, Physics, and Ethics. The 
Stoical Logic, while it had less admixture of Meta- 
physics than the Aristotelian', embraced on the other 
hand considerably more of Grammar and of Rhetoric. 
It was divided into two parts. Dialectic and Rhetoric, to 
which some added a third, the ogixov or doctrine of 
Definition, employed as a criterion of truth". Their 
Dialectic, which also contained a considerable mixture 
of Grammar, was defined as the science of rightly con- 
versing in question and answer, as Rhetoric was that of 
continuous speech. It is criticised by Cicero, as prolix 
in the treatment of judgment, deficient in that of inven- 
tion*. It also, particularly in the hands of Chrysippus, 
contained many of the same captious sophisms which 
had occupied the Megaric School. Their Rhetoric con- 
tained four parts. Invention, Elocution, Division, and 
Action. Cicero appears to have entertained no very 
high opinion of it". But of the details of the Stoical 
Logic very little is known ^. 
The Epi- The Epicureans, on the other hand, professed a con- 
tempt for Dialectic y, and regarded Logic, which they 
called Canonic, merely as an adjunct to physical science. 
They paid no regard to Syllogism, Induction, or Defi- 
nition, but confined their logical method to a set of 
rules for the investigation of physical truths A detailed 

■■ See Trendelenburg, Logische Untersuchungen, vol. i. p. 21. 

* Diog. Laert. vii. 41. 

' Top. 6. Be Orat. ii. 159. With these passages may be compared the 
following : 01 [i\v airh ttjs aToas 6pi^6/j.ej/oi r^u diaKeKTiK^v ^iTi(TTT)ixr)v tov eS 
\4yeiv opiCovTui, rh 5e ev Aeyeiv iv t^ TaXrjdri Kal irpoa-fiKovra Aeyeiv clvai 
ri6efjLevoi, rovro Se '[diou T]yovfxevoL tov (pi\o(T6<pov, Kara t7)s reAecoraTTjs (piKo- 
<TO<pias (pepovaiv avT6, koX 5ia tovto ix6vos 6 (piX6(TO(pos /cot' avrovs BiaXeKTiKSs. 
Alexander in Topica, p. 3. {Scholia, p. 251. a. 22.) 

1 De Fin. iv. 7. 

" St. Hilaire, Memoire, vol. ii. p. 135. 

y Laert. x. 31. Cf. Seneca, Ep. 89. 

^- Trendelenburg, Kategorienlehre, p. 232. 



INTRODUCTION. XXV 

iccount of these is given by Gassendi, De Origine 
Logicce^ c. 7. 

To the Philosophers succeeded the Commentators. The Greek 
These contributed but little new material to logical tators. 
cience, but did a good deal for the explanation and 
illustration of the text of Aristotle, and assisted in some 
degree in fixing the language of the science". The 
Greek Commentators on the Organon are principally 
aluable to a modern reader, from the interesting his- 
torical notices which they furnish of philosophers whose 
original contributions to the science have perished. 
Of the extant Greek Commentators, the earliest and 
best is Alexander of Aphrodisias^, whose eminence is Alexander, 
testified by the title of the Commentator (6 e^>37»3Tiljj), a 
title afterw^ards given to the Arabian Averroes. The 
school of Greek Commentators extends to the latter 
part of the sixth century : the principal writers, after Other 
Alexander, are Themistius, Ammonius, David the tators. 
Armenian, Simplicius, and Philoponus. 

The only important addition to the matter of logical Poriihyry. 
science emanated from the Neo-Platonic school. The 
elo-aywyij or Introduction to the Categories, written by 
Porphyry in the third century, is the original source of 
the fivefold classification of the Predicables, adopted by 
most subsequent Logicians. Whether this classification 
is an improvement on, or consistent with, the Aristote- 
lian doctrine, admits of considerable question*. 

* St. Hilaire, Memoire, vol. ii. p. 123, 14:5. 

b Gralen, in point of time, is a few years earlier than Alexander, but no 
important commentary of his is extant. Of the numerous logical writings 
attributed to him, there remains only a small treatise, Trepi tS>v irapa t)]v 
k4^i.v (To^KTixaTOiv^ the genuineness of which is questionable ; to which may 
be added the Elcraywyf) AiaXcKTiK^ recently discovered and published by 
M. Mynas. Neither is of any great logical value. Galen's invention of 
the fourth figure of Syllogism (attributed to him by Averroes) is doubtful. 
See below, p. 7o. note x. 

<= See below, p, 23. note q. 



XXV 



INTRODUCTION. 



Greek 

Abridg- 

meuts. 



Joannes 

Dama- 

scenus. 



Photius. 



Psellus. 



Blemmi- 
das. 



Pachy- 
meres. 

Leo Ma- 
gentinus. 



Georgius 

Trape- 

zantius. 



The Greek Abridgments of Aristotle, though in point 
of chronology they extend below the scholastic period, 
are in matter rather connected with the preceding series 
of Commentators. While the Scholastic Logic began 
in the extreme west of Europe, the Greek Logicians oi 
this class belong entirely to the extreme east, or to 
Asia. John of Damascus, in the early part of the eighth 
century, made a brief analysis of the Isagoge of 
Porphyry and of the Categories, and is remarkable as 
one of the first who applied Logic to Theology. Photius. 
the learned and turbulent Patriarch of Constantinople 
in the ninth century, was the author of abridgments of 
the Categories and the De Interpretation e. Michael 
Psellus the younger, in the eleventh century, composed 
a Synopsis of the Categories and of Porphyry's Intro- 
duction'^. The most remarkable work of this kind is the 
Epitome Logica of Nicephorus Blemmidas, written in the 
thirteenth century, which has been quoted as containing 
the earliest instance of that system of logical mnemonics 
which the schoolmen afterwards brought to such per- 
fection^. The list of Greek Logicians closes with the 
names of George Pachymeres of Constantinople, author 
of an abridgment of the Isagoge and the Categories; and 
of Leo Magentinus, Metropolitan of Mytilene, author of 
an Exegesis of the De Interpretatione, principally taken 
from Ammonius, and of Commentaries, some of which 
are still unpublished. To this list, some have added 
the name of George of Trebizond ; but he, though a 
Greek by birth, is better known as a resident at Rome, 
and, as an author, by his Latin translations and abridg- 
ments of Aristotle. His name is rather connected with 



^ The Synopsis of the Organou attributed to Pselhis is probably spimous, 
^ See St. Hilaire, Memoire, vol. ii p. 160. It may be questioned whether 
the Latin Logicians are indebted to the Greek in this respect. See Sir 
W. Hamilton's Discussions, p. 126, 6ol *, and below, p. 81. 



IiNTRODUCTION. XXVU 

a different phase of philosophy, with the Platonic and 
Aristotelian controversies in the time of Pope Nicholas V. 

The progress of Logic among the Latins presents in Latin Lo- 
one respect a contrast to that among the Greeks. With 
the latter, the age of abridgments and distinct treatises 
followed that of commentaries ; with the former, it 
preceded. The earliest work of a logical character in 
Latin is the abridgment of Aristotle's Topics by Cicero ; Cicero. 
the object of which, however, is rather rhetorical than 
dialectical. This treatise, which was written from 
memory, differs in many respects considerably from the 
original. After Cicero, we find nothing but a few 
allusions to the subject in Quintilian and Aulus Gellius', 
till we come to the short account of the doctrine of the 
De Interpretatione and the Prior Analytics, written in 
the second century by Apuleius. This occurs in the Apuleius. 
third book of his treatise De Dogmate Platonis ; and the 
singular error of attributing the syllogistic theory to 
Plato has caused the genuineness of this book to be 
questioned^. The only other logical writings in Latin Augustine, 
before Boethius, are the two works attributed to St. 
Augustine ; the one, an abridgment of the Categories, 
now generally allowed to be spurious, but probably 
written about the same period ; the other, an unfinished 
treatise called Principia Dialectica, the commencement 
of an essay on language with a view to disputation. 
To these must be added the singular allegory of Mar- 
cianus Capella, on the Marriage of Mercury and Philo- Capella. 
logy ; a medley of prose and verse, composed probably 
towards the end of the fifth century. The Seven Liberal 
Arts, afterwards so celebrated as forming the Trivium, 
and Quadrivium, or Encyclopaedia of the middle ages 
appear in the following order. Grammar, Dialectic, 

^ See St. Hilaire, Memoire, vol. ii. p. 165. 
8 Hildebraud, De Apuleii Sc7'iptis, p. xliv. 



XX VI 11 



INTRODUCTION. 



Rhetoric, Geometry, Arithmetic, Astronomy, and Music ^. 
Dialectic is represented as a female of a sour counte- 
nance, holding in her left hand a serpent, aud in her 
right a hook baited with sundry formulae. She discloses 
her wisdom by a brief abstract of the Isagoge of Por- 
phyry and of the first three treatises of Aristotle. This 
is followed by an account of hypothetical syllogisms ; 
and the lady is about to proceed to an exposition of 
sophisms, when she is interrupted and very summarily 
dismissed by Minerva. 

Boethius. Boethius, in the sixth century, is the only commentator 
proper among the Latins. He has left a considerable 
number of valuable logical works, viz. two commentaries 
on the Isagoge of Porphyry, one on the Categories, two 
on the De Interpretatione, and translations of the other 
parts of the Organon ; besides original treatises on the 
Categorical and Hypothetical Syllogism, on Division, on 
Definition, and on Topical Differences ; together with a 
commentary on the Topics of Cicero. His works are 
of great importance in the history of Logic. They form 
the connecting link between the Greek and Scholastic 
writings, and were, with those of Augustine and Capella, 
the principal authority of subsequent generations, at a 
time when the Greek la,nguage was but little cultivated, 
and when the original fountains of logical science were 
consequently inaccessible. 

Cassiodo- Contemporary with Boethius was Cassiodorus the 



h M. St. Hilaire has committed an oversight in citing the di\ision of 
the Seven Liberal Arts from the Dialectic of Augustine. No such di%ision 
occurs there ; though one nearly the same is found in his second Book 
De Oydine, ch. 13. M. Haureau {de la Philosophie Scholastique, vol. i. 
p. 21.) attributes the invention of this classification to CapeUa, which is 
hardly reconcileable with the above reference. The Seven Liberal Arts 
were afterwards exhibited in the following mnemonic : 

" Crram. loquitur, Dia, vera docet, Rket. verba colorat, 
Mus. canit, Ar. numerat, Geo. pouderat, Ast. colit astra." 



INTRODUCTION. XXIX 

Senator, the author of a Treatise on the Seven Liberal 
Arts. His Dialectic contains a brief analysis of the 
Isagoge of Porphyry and the Organon of Aristotle, with 
additions, a considerable portion being borrowed from 
Apuleius and Boethius. His analysis of the Organon 
does not include the Sophistic Refutations, but contains 
a separate chapter De Faralogismis, which treats of 
purely logical fallacies. The arrangement of the work 
is by no means methodical, and extraneous matters 
are introduced which properly belong to Rhetoric. 

The body of Arabian Commentators derive their ap- The 
pellation from the language in which they wrote : their coramen- 
places of residence were various, and none of them tators. 
within the limits of Arabia. In fact, the Arabian lite- 
rature did not arise till after the conquests of the suc- 
cessors of Mahomet had extended the Saracen empire 
far beyond the boundaries of their original country. 
Like the latter Greek Logicians, the Arabians contributed 
little original matter to the science; their principal works 
being either translations, made sometimes from the 
Greek but more frequently from the earlier Syriac 
versions, or abridgments and commentaries. Of these 
the most important are the logical abridgments of 
Aviceiina and Algazel, and especially the voluminous 
translations and commentaries of Averroes. A Latin Averroes. 
version of the translations of Averroes, made from a 
Hebrew one, was the principal source from which the 
earlier Schoolmen derived their knowledge of all the 
writings of Aristotle, except his logical works, which 
had been translated by Boethius. This barbarous ver- 
sion continued in use even after a more accurate trans- 
lation from the original Greek had been made by 
William of Moerbecke, under the direction of Thomas 
Aquinas. The merits of Averroes as a commentator 
have been variously estimated. Ludovicus Vivos speaks 



XXX INTRODUCTION. 

of him with great contempt. " Nomen est commentatoris 
iiactus, homo qui in Aristotele enairando nihil minus 
explicat quam eura ipsum quern suscipit declarandum." 
With this may be contrasted the eulogy of Keckermann. 
" Nemo tarn veterum interpretum videri potest proximus 
Aristotelis menti atque hie Arabs." The modern critic 
will probably take a middle course between the two. 
While his commentaries may be pronounced somewhat 
prolix, and inferior in elucidating the text of Aristotle to 
those of the Greeks, particularly of his rival commentator 
Alexander ; his general view of the Organon and its parts 
has much of the clearness which distinguishes the abridg- 
ments of Avicenna and Algazel'." 

The principal material added by the Arabians to the 
text of Aristotle is the celebrated distinction between 
first and second intentions. This is found in the Epitome 
of the Categories by Averroes. It has also been traced 
to Avicenna''. To the Arabians also are probably owing 
some of the distinguishing features, though certainly not 
the origin, of the Scholastic Realism. 
The The period at which the Scholastic Philosophy may be 

men. ^^^^ ^^ have commenced, is a point of considerable dis- 

Scholastic pute. It cannot, like various Greek schools of philosophy, 
sophy ^® traced to a single founder; but was the gradual result 
of a collection of various doctrines and methods of teach- 
ing. Some have traced it up to John of Damascus, and 
even to St. Augustine ^ Some commence with John 
Scotus Erigena in the ninth century, some with the 
nominalism of Koscelin in the eleventh""; while by others 
it has been brought down, at least as far as Theology is 
concerned, as low as the thirteenth century, the era of 

• St. Hilaire, Memoire, vol. ii. p. 191. 

^ See Smiglecii Logica, Disp. ii. Qu. 2. 

' Brucker, vol. iii. p. 716. 

'" Hallara, Literature of Europe, vol. i. p. 13. 



INTRODUCTION. XXXI 

Albevtus Magnus and Thomas Aquinas". The name of 
Schoolmen appears to have been taken from the teachers 
of the cathedral and conventual schools established by 
Charlemagne and his successors, and was eventually 
applied to all who, whether professedly teachers or not, 
adopted in their writings the method and matter which 
finally formed the course of education in these and similar 
establishments. The distinguishing feature of Scholas- 
ticism, the union of a theological matter with a dialectical 
method, is found at least as early as the writings of 
Lanfranc in the eleventh century. Commencing from 
this point. Scholasticism may be divided into three 
periods, 1. Its infancy, extending from the eleventh 
to the middle of the thirteenth century. 2. Its prime, 
from the latter period to the middle of the fifteenth. 
3. Its decline, extending to the end of the sixteenth 
century °. 

The Logic of the Schoolmen is a phrase frequently Scholastic 
employed, and often very inaccurately. It is incorrect ° 
to apply this name to the various applications of the 
syllogistic method, in Theology, in Metaphysics, in 
Phj^sics, or in Psychology. These are merely treatises 
on their proper subjects, with a somewhat more osten- 
tatious display of logical art than has been usual at 
other periods. But the applications of Logic to reason- 
ings on this or that branch of material science have 
nothing in them which is more peculiarly the property 
of the Schoolmen than of any other reasoners. The 
Logica uteris is one and the same to all generations of 
men ; all who reason soundly, reason consciously or 
unconsciously by logical laws, and the open display of 
the instrument in use does not make it a distinct in- 



" Hampden, Bampton Lectures, p. 72. 

" Cousin, Ouvrages d'Ahelard, Introduction, p. Ixv. 



XXXll INTRODUCTION. 

strumeiit from that which others employ in a more 
concealed manner. 

A historical account of the Scholastic Logic ought 
therefore to confine itself to commentaries and treatises 
expressly on the science ; and the scholastic contri- 
butions to the matter of Logic should be confined to 
such additions to the Aristotelian text as have been 
incorporated into the Logica docens. In this respect 
the Schoolmen did much to fix the technical terms of 
the science, particularly in respect of the relation of 
thought to language. Most of the distinctions of the 
different uses and significations of words are due to 
them ; — distinctions, however, carried to an useless and 
wearisome minuteness in the grammatical subtleties of 
the parva logicalia. They also contributed considerably 
to that which is most wanting in Aristotle, an exact 
conception of the nature and oflice of Logic ; though 
their definitions were not always consistent with the 
rest of their treatment; the text of Aristotle being 
seldom modified to suit the theory of the science. But 
the most remarkable contribution of this period is to 
be found in that singular system of logical mnemonics 
by which, from the time of Petrus Hispanus, nearly all 
the forms and processes of Logic might be learned by 
rote and performed almost mechanically, by the aid of 
a memorial word or line. The controversy between the 
Realists and the Nominalists, though introduced into 
the pages of professedly logical treatises, cannot be 
regarded as an accession to the science. Its real 
bearings on the text of Aristotle and Porphyry were 
not seen by the disputants on either side^; and the 
controversy, as conducted by them, must be regarded as 
a metaphysical excrescence, introduced out of its place 
in a logical system. 

p See p. 24, note r, and Appendix, note A. 



INTRODUCTION. XXXlll 

The earliest scholastic writings on Logic proper are Abelard. 
those of Abelard, the greater part of which have recently 
been published for the first time by M. Cousin. They 
consist of glosses on the original and translated works 
of Boethius, a fragment on Genera and Species, and a 
distinct treatise called Dialectica'^. The glosses are of 
little value, but the Dialectica is one of the most im- 
portant monuments of the scholastic philosophy. At 
first sight it appears to be a commentary; but, though 
the titles of the work follow Aristotle, Porphyry, and 
Boethius, it is in many respects an original and in- 
dependent treatise ^ It appears clearly from these relics 
that Aristotle was only known in the twelfth century 
through the translations and commentaries of Boethius. 

Contemporary with Abelard was Gilbert de la Porree, Gilbert de 
, r« T» • • • • /. -I • 1 1^ Porree. 

whose bex Frincipia^ an expansion oi the six last 

categories cursorily treated by Aristotle, was adopted in 

most of the scholastic logical treatises down to the 

sixteenth century ^ 

Towards the end of the twelfth century w^e come John of 

to a work of great importance in the history and 

philosophy of the scholastic Logic, the Metalogicus 

of John of Salisbury. The work purports to be a 

defence of Logic, under which is included Grammar and 

Rhetoric, against a sciolist of the day, to whom he gives 

the name of Cornificius'. It contains an interesting 

account of the author's own preparation for dialectic 

q A theological treatise called Sic el Non is contained in the same 
volume. 

■■ Cousin, Introduction, p. xxiii. 

s Haureau, Philosophle Scholastiqve, vol. i. p. 298. 

t This name, M. Haureau explains as follows. " Cornifex, Cornificius, 
signifiera ' celui qui fait des cornes.' Mais de quelles cornes peut-il 
etre ici question ? Sans doubt de ces cornua dispvtationis dont parle encore 
Ciceron; ce qu'on appelle, en logique, les cornes d'un dilemme. A ce 
compte, nos Cornificiens auraient ete d'aigres disputeui's, des logiciens 
aceres, d'intraitables sophistes." Philosophic Scholastique, p, 344. 



XXXIV INTRODUCTION. 

Studies, notices of the origin of Logic, and a good 
analysis of the Organon with criticisms. Among other 
points, it is worthy of notice that he considers the 
Aristotelian doctrine of the predicables, given in the 
Topics, to be preferable to the common account, derived 
from Porphyry. He highly praises Abelard ; and his 
testimony is the more valuable, as he himself appears 
to incline to the doctrines of the Realists". 
Petrus In the second period of Scholasticism, contemporary 

* with Albertus Magnus and Thomas Aquinas, is Petrus 
Hispanus, raised to the papal chair as John XXT. He 
died in 1277. His Summulce Logicales may be regarded 
as the earliest scholastic treatise on Logic which professes 
to be any thing more than an abridgment of or commentary 
on portions of the Organon. But this work is especially 
remarkable, as introducing for the first time the memorial 
verses which form so striking a feature of the Logic of 
the Schoolmen. Nearly the whole of the ordinary logical 
mnemonics occur in this treatise, which appears to have 
had no predecessor, except perhaps the imperfect syllo- 
gistic mnemonic attributed to Blemmidas, which, even if 
genuine, was probably unknown to the Author'. The 

1 St. Hilaire, vol. ii. p. 215. His opinions in this respect however ai-e 
douhtful. See Haureau, vol. i. p. 354. 

* In the first edition, I mentioned the Summulce Logicales as a translation 
from the Greek of Psellus, This charge has heen made by Keckennann 
and Buhle ; and the two works certainly correspond ahnost to a word. But 
from a communication with which I have been favoured by Sir William 
Hamilton, I am inclined to think that the reverse is the truth ; that the 
Greek work is in reahty translated from the Latin ; and of course in that 
case falsely attributed to Psellus. The author of the Summulge appears to 
have had very httle knowledge of Greek ; and in the only mnemonic which 
occurs in the Greek sjoiopsis {5ov\ov/xeyaL IXidSes irapvacriov iKTp4xov(ri) , 
the diphthong would hardly have occmred to an original -vsiiter ; though 
a natural substitute for the Purpurea Iliace Amabimus EdentuU of the 
Latin Logicians. Indeed, the name of Psellus appears to have been given 
on conjectm-e by the editor, Ehinger. Some remarks on this point will be 
found in the Discussions on Philosophy, by Sir W. Hamilton, p. 126. [See 
also the 2d Edition of the same work, p. 67J .] 



INTRODUCTION. XXXV 

last treatise of the Sunimiilaey, called Purva Logicaliay 
contains sundry additions to the text of Aristotle, in the 
form of dissertations on supposition ampliatio, restrictio, ex- 
pordhle propositions, and other subtleties, more ingenious 
than useful, and belonging rather to Grammar than to 
Logic. To these are added notices of some popular 
sohpisms, worthy of Eubulides or Chrysippus ; which 
are curious, as shewing that the Scholastic Logic, like 
the Aristotelian, had its eristic predecessors, whose 
names the reviving literature of the period has not rescued 
from oblivion. 

We now come to the two chief names in the Scholastic Albertus 
philosophy, Albert of Cologne, surnamed the Great, ^^""^' 
and his pupil, Thomas Aquinas, known as the Angelic 
Doctor. These have been called the Plato and Aristotle 
of Scholasticism ; and, as regards the Theology of the 
Schools, there is some truth in the comparison. The 
master was the first to combine into a system of the 
unconnected reasonings which formed the beginnings 
of the School Philosophy. The disciple carried out 
that system in detail, and elaborated its minutest parts ^. 

As a commentator, Albert was the main instrument 
in introducing the writings of Aristotle into the Schools; 
his laborious expositions, however, have been frequently 
corrupted by Platonic and Arabian glosses ^ His logical 
works are comprised in commentaries on the Organon, 
and treatises on Universals and on Definition. Aquinas Aquinas. 
has left also commentaries on the Hermeneia and 
Posterior Analytics ; and some independent logical y^. 

treatises ; the principal one being " Summa totius vJ^ 

y The original edition of the Summulae is di\ided into two parts ; the 
abridgment of the Organon and the Parva Logicalia. Subsequent Editors 
subdivide it into seven treatises. See Haui'eau, vol. ii. p. 241. 

^ Encyclopaedia Metropolitana, art. Aquinas, (by Bishop Hampden,) 
p. 796. 

* See Haureau, vol. ii. p. 10. 



^ 



XXXVl INTRODUCTION. 

Logicae," which contains an abstract of the Isagoge of 
Porphyry and of the first four treatises of the Organon. 
The Topics and Sophistic Refutations are omitted in 
this work ; but the latter form the basis of a sejDarate 
treatise on the Fallacies. He has likewise written 
Opuscula on Demonstration, on Modals, on the four 
Opposed Terms, on Genus and Accident, and on the 
Nature of the Syllogism. The directly logical writings 
of Aquinas do not materially differ from Aristotle. Logic, 
however, is defined as scientia rationalis, and the three 
operations of the reason are brought within its province. 
Some of the mnemonic formulae occur here, as in 
Hispanus. 
Duns John Duns Scotus, the Subtle Doctor, flourished at 

Scotus. ^i^g g^j Q^ ^^ thirteenth and the beginning of the four- 
teenth century. He has commented on the Isagoge of 
Porphyry, under the title of De Universalibtis, and on 
the several parts of the Organon. In common with 
Aquinas, he held Logic to be a science ; but maintains 
that its object is not the three operations of the reason, 
but the Syllogism^. His commentaries bear out his 
cognomen; consisting for the most part of minute dis- 
tinctions, suggested by the text of his author, with argu- 
ments on both sides precisely stated, and distinctions 
drawn to the extreme of subtlety. Scotus, like Aquinas, 
was a Realist, and the more consistent of the two. He 
held that the universal existed in the individual, not 
really, as his predecessor had taught, but formally". 
Hence the rival sects of Thomists and Scotists, the latter 
of whom ultimately adopted the name of Formalists. 
Both agreed, however, in opposition to Nominalism. 
Occam. From the school of Scotus, however, arose the great 

reviver of Nominalism, William Occam, the Invincible 

*» Scotus de Univ. Qu. 3. Smiglecii Logica, Disp. ii. Qu. 1. 
<= On this distinction, see Haureau, vol. ii. p. 335. 



INTRODUCTION. XXXVU 

Doctor, the ablest writer in Logic whom the Schools 
have produced. His doctrine, like that of Abelard, was 
really Conceptualisrn*^. The Summa totius Logicce of 
Occam is the most valuable contribution of the middle 
ages to the Logica docens. If we do not subscribe to the 
hyperbole of his editor, Mark of Beneventum, w^ho, 
borrowing from the well-known eulogy of Plato, declares 
that if the Gods used Logic, it would be the Logic of 
Occam, we may fairly allow, with M. St. Hilaire, that it 
is the clearest and most original of the works of that 
period. Occam, like Petrus Hispanus, departs from the 
ordinary arrangement of treating consecutively the Isa- 
goge of Porphyry and the several books of the Organon. 
He commences with the different divisions of terms, of 
which his account is much more complete than that of 
the Summulce Logicales, He then proceeds to the pre- 
dicables, introduced by a defence of the nominalist view 
of universals, then to definition, division, and the cate- 
gories, and concludes the first part with an account of 
the supposition of terms. The second part treats of 
propositions, and the third of syllogisms and fallacies. 

Between Scotus and Occam comes in order of time Raymond 
the most eccentric genius of the scholastic period, Ray- ^' 
mond Lully. He is principally known as the author of 
the Ars Magna, by which he professed to teach a man 
ignorant even of letters the whole encyclopaedia in the 
course of three months. This work is nominally logical, 
but has little in common with the Aristotelian Logic, 
being principally a mechanical contrivance for connect- 
ing different philosophical terms with each other®. But 
in his Dialectica, Lully condescends to follow the 
beaten track, and has composed a clear and concise 



^ See Cousin, Abelard, Introduction, p. civ. 
*^ St. Hilaire, Memoire, vol. ii. p. 225. 

d 



XXXVlll 



INTRODUCTION. 



Later 

School 
men. 



synopsis of Logic, framed principally on that of Petnis 
Hispanus^ 

The writings of Occam, as well as those of Scotus, con- 
tributed especially to raise Logic to the rank of a distinct 
science, independent of its applied uses^. But they 
approached it from opposite sides. The principles of 
Occam, developed by modern philosophy, would lead us 
to the Logic of Kant: those of Scotus, almost to the 
Logic of Hegel. The science of the former would 
acquire a clear and distinct object in the province of 
Thought : that of the latter would gradually absorb all 
else, as coextensive with Being. Occam is the last great 
name among the Schoolmen : the triumph of Nominalism 
involved the downfall of the principal applications of 
Bmidan. the scholastic method. Buridan, his disciple, the reputed 
author of the sophism called Asinus Buridani^, deve- 
loped the doctrines of Nominalism to a still further 
extent, but has the character of having pushed to an 
extreme point the subtleties distinctive of the scho- 
lastic system. Another philosopher of the same period, 
Walter Burley, is the author of some commentaries on 
the Logic of Aristotle, and deserves mention as the first 
compiler of a history of philosophy. This work is 
entitled, de vita et morihus philosophorum, and forms a 
biographical history of philosophy from Thales to 
Seneca'. 

f An account of Lully's system will be found in Keckermann, Prceeognita, 
ii. 2. 39. and in Gassendi de Origine Logicce, c. 8. See also Hallam, 
Literature of Europe, vol. i. p. 310. 

s Cf. Haureau, vol. ii. p. 310. 425. 447 sqq. St. Hilaii-e, vol. ii. p. 226. 
M. Haureau appears to regard Scotus as the author of the distinction 
between the logica docens and utens ; which is not the case. Cf. Aquinas, 
in iv. Metaph. Lect. 4. Indeed, it is substantially contained in the 
SiaKeKTiK^ X'*'P^5 irpay/xdrwu and iv xp^^^^i- irpayixdrwv of the Greek Inter- 
preters. 

h See Hamilton on Eeid, p. 238. 

' Brucker, vol. iii. p. 856. Burley appears to have held a middle course 
between Nominalism and Realism. See Ham-eau, vol. ii. p. 476. 



Burley. 



INTRODUCTION. XXXIX 

The reaction against the Scholastic Logic began in Early Re- 
the fifteenth century. Laurentius Valla, Rodolphus 
Agricola, and Ludovicus Vives, successively attacked 
the system in 1440, 1516^, and 1531. Their attacks 
were directed, partly against the Latinity, partly against 
the matter of the School Logic. The additions proposed 
by these reformers are chiefly rhetorical innovations 
from Cicero and Quintilian. 

A more formidable assault was made in 1543 by Ramus, Ramus. 
who not only devoted a special work to the criticism of 
Aristotle^, but, adopting the dialectical and rhetorical 
innovations of the earlier reformers, composed a new 
system of Logic in opposition to the Aristotelian. He 
complains of the want of a definition of Logic in 
Aristotle, and treats it himself as the Art of Disser- 
tation ; its principal parts being Invention and Judgment. 
These he investigates at length in his Dialecticce In- 
stitutiones and Scliolce Dialecticce, and in his Dia- 
lectique, the earliest work on the subject in the French 
language. Invention he treats chiefly rhetorically, 
giving an account of arguments artificial and inartificial, 
and loci for establishing them. Argument in Ramus 
denotes any term of a question, not, as in Cicero, the 
middle. Of Judgment he admits three degrees, Axiom, 
(proposition,) Syllogism, and Method. In the earlier 
editions of his Dialectic he admits the three Aristotelian 
figures, but afterwards rejects the third. Each figure 
has six moods, two general (universal), two special (parti- 
cular), and two proper (singular). Method he divides 
into Methodus Doctrince, and Methodus Prudentice. He 
rejects, as extralogical, the Categories, the Hermeneia, 

i Agricola died in 1485. His three books De Inventione Dialectica were 
a posthumous work, first published in an imperfect form at Louvain in 
1516. 

^ Aristotelicee Animadversiones, a title also given to the Scholce Dialecticce. 
The two works must not be confounded together. 

d2 



xl 



INTRODUCTION. 



Melanch- 
thon. 



and the Examination of Fallacies. Ramus, as may be 
seen even from the above cursory notice, introduced 
many needless alterations in the language of Logic, 
In his logical innovations, he is partly indebted to 
Rodolphus Agricola and Joannes Sturmius ; and, for 
some of his attacks on the Aristotelians, to Valla and 
Vives\ 

On the other hand, the Aristotelian Logic, purified of 
many of its scholastic accessions, was defended and 
taught by Melanchthon. The earlier editions of his 
Erotemata Dialectica preceded the attacks of Ramus": 
but in 1547 he published a new edition, in the intro- 
duction to which he says, " Ego veram, incorruptam, 
nativam Dialecticen, qualem et ab Aristotele et aliquot 
ejus non insulsis interpretibus, ut ab Alexandro Aphro- 
disiensi et Boethio accepimus, prsedico. . . . Etsi multi 
Aristotelicos libros vituperant, et tanquam tabulas dis- 
persas fractse navis esse dicunt, tamen, si quid ego 
judicare possum, affirmo eos Dialecticen recte tradere, 
et ab iis, qui liberali doctrina exculti sunt, intelligi 
posse." Melanchthon however agrees with Ramus, in 
considering Logic as an Art. " Dialectica," he says, "est 
ars seu via recte, ordine, et perspicue docendi ; quod fit 
recte definiendo, dividendo, argumenta vera connectendo, 
et male cohserentia seu falsa retexendo et refutando." 
Under their united sanction, this became the prevailing 
doctrine of Logicians. The authority of Melanchthon 
established the Aristotelian Logic in the Protestant 
schools of Germany and Holland, and in Britain. At a 
later period, a conciliation was attempted between this 
Later system and that of Ramus. Burgersdyck, in 1626, 
Logicians, classes the Logicians of his day in three schools, the 



1 For a fuller account of Kamus and his system, see Waddington- 
Kastus, Be Petri Rami Vita, Scriptis, Philosojjhia, Paris, 1848. 
ra Keckermann Prescognita, Tr. ii. c. v. 



INTRODUCTION. xli 

Aristotelians, the Ramists, and the mixed school repre- 
sented by Keckermann, Aristotelian in matter, Ramist 
in method". These were called Philippo-Ramists, or 
Semi-Ramists ; and were rejected by the genuine dis- 
ciples of Ramus, as Pseudo-Ramists. Among the English 
Ramists of the seventeenth century, the most learned 
and important as a Logician is George Downame, Downame. 
Bishop of Derry, author of a Commentary on the Dia- 
lectic of Ramus ; but the name most interesting to the 
general reader is that of John Milton, who published Milton. 
in 1672, two years before his death, a small volume 
entitled, " Artis Logicae Plenior Institutio ad Petri Rami 
Methodum concinnata." 

It would be impossible to give any thing like a 
complete history, or even a list, of the host of logical 
wTiters of the sixteenth and subsequent centuries. A 
brief account of most of them, down to his own time, will 
be found in the Prcecognita of Keckermann, published 
in 1603. A cursory account of the modern schools is 
all that my present limits will allow. 

Of the great schools of modern philosophy, down to Modern 
the time of Kant, it is remarkable, that, though we have ^ 
no treatise on Logic from the hand of any of the leaders 
and representatives of the several sects, we find in every 
case a work of the kind supplied and adapted to their 
fundamental principles by one or more of their most 
eminent followers. Bacon, Descartes, and Locke have 
left no logical writings, and Leibnitz only a few frag- 
ments. To call the Novum Organum^ or the Discours de 
la Methode^, or the Conduct of the Understanding, a 

" Of these, Sanderson says, " Invehimtur ipsi palam in Eameos, lau- 
dant Peripateticos : sed tamen in Systematibus suis Logicis Ramei magis 
sunt quam Peripatetici." 

° The RegulcB ad directionem inyenii, a posthumous work of Descartes, 
is sometimes called his Logic. See Hallam, Literature of Europe, vol. ii. 
p. 454 ; Franck, Histoire de la Logique, p. 250. But Descartes in this work 



Xlii INTRODUCTION. 

treatise on Logic, is simply to assume for the Aristotelian 
Logic a purpose never contemplated by Aristotle or his 
followers, and then to classify under the same head 
works pursuing this supposed end by totally diiferent 
means. To entitle any work to be classed as the Logic 
of this or that school, it is at least necessary that it 
should, in common with the Aristotelian Logic, adhere 
to the syllogistic method, whatever modifications or 
additions it may derive from the particular school of its 
author. Li this point of view, the Baconian school may 
be represented by the Logics of Hobbes and Gassendi; 
the Cartesian, by those of Clauberg and Arnauld; that of 
Locke, by Le Clerc and 'S GravesandeP; that of Leibnitz, 
by Wolf, Baumgarten, and his editor Meyer. 
Hobbes. The Logic of Hobbes was the natural result of the 
utilitarian spirit predominant in the method of Bacon. 
The results, indeed, which Hobbes deduced, would pro- 
bably in many points have been rejected by his master; 
but the indirect influence of Bacon is manifest through- 
out. The end of knowledge, according to Hobbes, 
is power, and the scope of all speculation is the perform- 
ance of some action, or thing to be done. In this we 
recognise the echo of the words of Bacon, " Meta scien- 

expressly rejects the rules and forms of Logic, as useless for the discovery 
of truth, and mentions in one place (rule 13.) the only point in which his 
system has any thing in common with the dialecticians. In fact, this work, 
though fuller, is in principle the same as the Discours de la Methode. 

P The sensationalist school of France, professing to be an oflfshoot of that 
of Locke, has produced more than one treatise nominally on Logic ; the 
principal ones being those of Condillac and Destutt de Tracy. But 
these have nothing in common with the Aristotelian system. Condillac 
regards Logic as an art of thinking, but thought is identified with sensation, 
and the process of reasoning is nothing but the analysis of our sensations 
by means of language. Hence his declaration, tout I'art de raisonner se reduit 
a I'art de Men parler. In the system of De Tracy, Logic is the science of 
the characteristics and causes of truth and error in the combination of 
our ideas. His work is strictly psychological, examining, on the extreme 
sensationalist hypothesis, into the formation of ideas and their different 
modes of combination. 



INTRODUCTION. xHu 

tiarum vera et legitima non alia est quara ut dotetur vita 
humaiia novis inventis et copiis''." Reasoning, accord- 
ing to Hobbes, is computation, the adding and sub- 
tracting of our thoughts and of their signs. A pro- 
position is but the addition of two names, and a 
syllogism the adding together of three. In a proposition, 
two names are so coupled together, that he that speaks 
conceives both to be names of the same thing ; from 
whence it follows that truth and falsehood consist only 
in speech, and that the first truths were arbitrarily 
made by those who first imposed names on things. A 
full criticism of this doctrine would exceed my present 
limits. I can only observe that the main error of Hobbes 
does not lie, as is sometimes said, in his theory of notions, 
but in that of judgments. He has overlooked the fact, 
that apprehension is primarily the analysis of judg- 
ment, not judgment the synthesis of apprehensions. 

The Baconian influence is also manifest in Gassendi, Gassendi. 
the friend of Hobbes and the antagonist of Descartes. 
Like Hobbes, he describes reasoning as a computation, 
and he anticipates Condillac in tracing all knowledge 
to sensation. He adopts the fourfold division of Logic, 
into Apprehension, Judgment, Reasoning, and Method, 
which had virtually been invented by Ramus and 
accepted by the Semi-Ramists, and which was shortly 
afterwards adopted by the Port Royal Logic. He 
admits two figures only of Syllogism, an affirmative 
and a negative, (answering to the affirmative and nega- 
tive moods of the first figure in Aristotle ;) and it is worthy 
of remark, that in the order of the premises, he returns 
to the arrangement of the Greek Logicians, (the reverse 

^ Nov. Org. P. 1. Apli. 81. In the same spirit Socrates, according to 
Xenophon, fxexpt tov w^eAt/U*"' irdura Koi avrhs (rweTr€(TK6ir€i kuI avvSie^'pei 
roh (Tvvovffiv. Mem. iv. 7. On the influence of Bacon on Hobbes, see 
Morell, Hist, of Modern Philosophy, vol. i. p. 86. 



Xliv INTRODUCTION. 

of tha? of the Latins,) and places the minor before the 
major. His theory of reduction, by which he brings 
every syllogism ostensively to his two figures, contains 
some curious blunders. 

Clauberg. Clauberg, called by Wolf optimus omnium eonfessione 
Cartesii interpres"^ , published his Logica Vetus et Nova 
in 1654. It contains more of Cartesianism even than the 
Port Royal Logic, and is divided into four parts, Logica 
Geiietica, Logica Analytica, Hermeneutica Genetica, and 
Heimeneutica Analytica, The two last parts are a series 
of rules for interpreting and criticising the writings 
of others. The second treats of methods of teaching, 
and the qualifications for a good teacher and learner. 
The first, or Logic proper, is interspersed with numerous 
psychological precepts, chiefly taken from the Discours 
de la Methode of Descartes. Many of his examples are 
also taken from the Cartesian philosophy. His rules for 
induction are fuller than in the old Logic, and those of 
syllogism shorter. 

Port Eoyal The Port Royal Logic, or Art of Thinking, is con- 
sidered as the Logic par excellence of the Cartesian 
school. This work has been attributed to several 
authors ; but is now generally allowed to have been 
written by x4rnauld, assisted by Nicole. The first 
edition appeared in 1662. In addition to the logical 
merits of this work', the elegance and simplicity of its 
style contributed immensely to spread and popularize 
doctrines which had hitherto been reserved for the study 
of the learned in the dry formulas of the schools *. The 
authors, however, must be admitted to have sacrificed 
in some degree scientific accuracy to popularity ; and 

r Ontologia, §. 7. 

* For an account of the scientific merits of the Port Eoyal Logic, see the 
Introduction to Mr. Baynes's Translation, p. xxix. 
' St. Hilaire, vol. ii. p. 271. 



INTRODUCTION. xlv 

in their attempt to convey miscellaneous instruction in 
logical examples, they have unfortunately given their 
high authority to the support of that spurious utili- 
tarianism which has so often defaced the simplicity of 
logical science. 

Father Buffier is also entitled to honourable mention Buffier. 
among the French Logicians. In his Priyicipes du 
Raisonnement, the rules of the syllogism are reduced to 
a single principle, that which is in the co7itained is in the 
containing. This formula, an important step towards 
the true law of syllogism, the Principle of Identity, is 
perhaps originally due to Leibnitz". Buffier has had 
the good fortune to receive high praise from two very 
opposite quarters, and on very different grounds. He 
has been celebrated, on the one hand, as one of the 
earliest who attempted to found philosophy on certain 
primary truths, given in certain primary sentiments or 
feelings ; and, on the other hand, as having advanced 
some important steps in the direction of the sensa- 
tionalism of Condillac\ 

Le Clerc, (Joannes Clericus,) the friend and disciple Le Clerc. 
of Locke, published his Logic in 1692, three years after 
the first edition of Locke's Essay, of which he had 
previously seen the Epitome. This work is principally 
based on the views of Locke, with some additions from 
the Port Royal Logic, and the Recherche de la Verite 
of Malebranche. The fourth book, on Argumentation, 
does not materially differ from the Aristotelian view ; 
though, like Locke, he has not a high opinion of the 
syllogism, and considers it to be mainly an instrument 
of disputation. He adds a chapter on the Socratic 
method of discussion, which he considers more valuable 

« See. St. Hilaire, vol. ii. p. 274. 

^ See Hamilton on Eeid, p. 786. and Destutt-Tracy, -E/emens d' Ideologic, 
P. iii. p. 130. 



Xlvi INTRODUCTION. 

than the Aristotelian syllogism. The Logic and Meta- 
'S Grave- phvsics of 'S Gravesande, published in 1736, is highly 

sande. 

praised by M. St. Hilaire, as simplifying with great 
clearness the ancient Logic, in connection with the 
principles of Locke. The doctrines of Locke, modified 
by Cartesianism, had also considerable influence on the 

Watts. Logic of Watts, in which a somewhat incongruous union 
of Logic, Metaphysics, Psychology, and Educational Pre- 
cepts is put forth as the Art of using Reason well in our 
inquiries after truth, and the communication of it to others. 
Equally vague in its conception and unsystematic in its 

Bentham. contents is the fragment on Logic by Jeremy Bentham. 
According to his definition. Logic is " the art which has 
for its object or end in view, the giving, to the best 
advantage, direction to the human mind, and thence to 
the human frame, in its pursuit of any object or purpose 
to the attainment of which it is capable of being applied." 
In the same spirit as Hobbes, he considers Logic from 
the utilitarian point of view, as a means to the augment- 
ation of happiness. But the treatise, except as regards 
some severe and by no means just criticisms of San- 
derson, has little in common with the Aristotelian system. 
A more just and philosophical view of Logic will be 

Kirwan. found in the works of another English writer. Dr. Kirwan, 
whose " Logic, an Essay on the elements, principles, and 
different modes of Reasoning," was published in 1807. 
Dr. Kirwan deserves honourable mention as one who 
has profited by, without servilely following, the teaching 
of Locke. While adopting much that is valuable in 
the writings of Locke and his successors, particularly 
Berkeley and Condillac, he has ably defended the 
Aristotelian Logic against the depreciating criticisms of 
Locke and his followers. He has however taken too 
narrow a view of the field of Logic, in confining it to the 
single process of Argumentation, in which, as well as in 



INTRODUCTION. xlvii 

his definition of it as both a Science and an Art, he has 
been followed by Archbishop Whately ; while, on the 
other hand, his treatment of the argumentative process 
contains much which from the formal point of view must 
be condemned as extralogical. 

The most important work on Logic from the school Wolf. 
of Leibnitz is the Philosophia Rationalis of Wolf, first 
published in 1728. Wolf is regarded by Kant as the 
representative of the dogmatic philosophy. Philosophy 
with Wolf is the science of things possible, so far as 
they are possible, and contains three principal branches. 
Theology, Psychology, and Physics. The criterion of 
the possible is the principle of contradiction. Whatever 
is not contradictory is possible". Logic directs the 
mind in the knowledge of all being ; its principles being 
drawn on the one side from Ontology, on the other 
from Psychology. The Logica Docens is defined by 
Wolf as a Practical Science ; the Logica Utens as an 
Art; the former being acquired by teaching, the latter 
by practice. The details of Wolf's Logic are principally 
Aristotelian, with one or two ingenious but perverse 
refinements. Thus, he reduces subaltern opposition to 
a syllogism with an identical minor premise, and all 
immediate consequences to abridged hypothetical syl- 
logisms. Induction he regards, like Archbishop Whately, 
as a s3dlogism with the major premise suppressed. Wolf 
is also the author of a smaller Logic in German, of which 
there is a good English translation, published in 1770. 

To the same school as Wolf belong Baumgarten and Baum- 
Meyer. Baumgarten is highly praised by Kant for his Meyer! 
concentration of the Wolfian system. An annotated copy 
of Meyer's Logic is the foundation of that of Kant 
himselfy. 

'^ On this criterion, see Hamilton on Reid, p. 377. 

y See the Preface to Rosenkranz's edition of Kant's Logic. 



Xlviii INTRODUCTION. 

Lambert. Lambert, whose Neues Organon appeared in 1764, 
may be regarded as uniting in a great measure the 
doctrines of the antagonist schools of Locke and Leibnitz, 
and as the precursor of the Critique of Kant. His 
system is divided into four principal parts, contributing 
conjointly to the investigation and communication of 
truth : Dianoiology, or the doctrine of the laws and 
power of the understanding in thought ; Alethiology, or 
the doctrine of truth as opposed to error; Semiotic, or 
the doctrine of signs and their influence to the know- 
ledge of truth ; and Phenomenology, or the doctrine of 
false appearances and the means of avoiding them. In 
his first part, he principally follows Wolf, but differs 
from him in his view of the Syllogistic figures ; the 
three last figures being regarded as resting on inde- 
pendent axioms, coordinate with the dictum de omni et 
nullo. These axioms are distinguished as dictum de 
diverse, dictum de exemplo, and dictum de reciproco. In 
his second part, which treats of simple and complex 
notions, and of truth and error, Lambert acknowledges 
his obligations to Locke. Li the third, the theory 
of language and its relation to thought is treated with 
considerable fulness. The fourth part, which treats 
of appearance as distinguished from reality, has more 
of a metaphysical and psychological than of a logical 
character, with some mixture of physiology. 

Ploucquet. Another German Logician who deserves mention, not 
so much for the importance as for the eccentricity of 
his views, is Godfrey Ploucquet of Tubingen, a con- 
temporary of Lambert's, the author in 1768 of a " Me- 
thodus calculandi in Logicis," afterwards included with 
other writings in his " Commentationes Philosophicae 
selectiores," published in 1781. Ploucquet's work is re- 
markable as an attempt to exhibit the reasonings of Logic 
in the form of an algebraical calculus, an attempt recently 



INTRODUCTION. xllX 

carried out to a greater extent by the " Neue Darstellung 
der Logik" of Drobisch, and in the logical writings of 
Professors De Morgan and Boole. A severe criticism of 
the principle of Ploucquet's Calculus will be found in 
Hegel's Logic, vol. ii. p. 143. The geometrical illus- 
trations of the syllogism by Euler and Lambert are not 
of sufficient importance to require a separate notice. 
An account of these, as well as of Ploucquet's system, 
is given in the Appendix to Professor De Morgan's 
" Formal Logic," p. 323. 

Kant has done more for logical science than any Kant, 
philosopher since Aristotle; partly in his distinct 
treatise on the subject, and still more in the exact 
examination of the forms and functions and limits of 
thought which runs through the Critique of Pure Reason. 
To Kant is owing, what has been so long needed, a 
definition of Logic, which secures for it a distinct and 
positive field of inquiry, as the Science of the Necessary 
Laws of Thought. Kant also did great service in 
banishing to a separate region, under the name of 
Applied Logic, the psychological precepts which his 
predecessors, especially the Cartesians, had incorporated 
with the body of the science, and giving thereby to 
formal thought its proper position as the object of Pure 
Logic. His demonstration that an universal material 
criterion of truth is not only impossible, but self-con- 
tradictory % has furnished us with the principle of a 
more liberal and enlightened appreciation of the real 
character and value of formal thinking than can be 
supplied by the whole previous history of philosophy. 

At the same time, it must be admitted that the logical 
system of Kant is chargeable with one serious deficiency, 
which has been prominently shewn in the subsequent 

* Logik, Einleitmig, vii. 



1 INTRODUCTION. 

history of the science. He divorces altogether his d 
priori science from all connection with the psycho- 
logical phenomena of consciousness, from all examination 
of the actual characteristics of any determinate operation 
of thought^ These matters he rejects as empirical; but 
without such empiricism, Logic and all pure science is 
impossible. It is matter of each man's personal experi- 
ence that he actually thinks; and, without examination of 
the phenomena of special acts of thought, it is impossible 
to ascertain the necessary laws of thought in general^. 
Logic and Psychology thus necessarily form portions 
of one and the same philosophical course, and, without 
a knowledge of the latter, it is impossible to have any 
sound criticism or accurate estimate of the former. 
Later The writings of Kant have had immense influence on 

LoSSns. *^^ subsequent Logic of Germany. It is true that 
the two greatest of his immediate successors, Fichte and 
Schelling, have produced no direct logical work ; and 
have openly expressed their low estimate of the sciences 
But a host of able writers have notwithstanding arisen, 
as numerous as the Logicians of the sixteenth and seven- 
teenth centuries, to promulgate, to correct, or to oppose 
the Kantian Logic. Some of these, as HofFbauer and 
Kiesewetter, adhere for the most part to the Kantian 
limits. Others, as Krug and Fries, are mainly Kantian, 
though they have materially enriched the science from 
their own resources ; and the latter has especially noticed 
the want of a psychological relation, as the main defect 



* See Kritik der r. V. p. 58, 276. ed. Eosenkranz. 

^ Cf. Cousin, Lemons sur Kant, p. 180. 

c FicMe, in his " Vorlesungen ueber das Verhaltniss der Logik zur 
Philosophie," altogether repudiates the ordinary Logic to make way for 
a transcendental system, and complains that this was not sufficiently done 
by Kant. Schelling in his " Bruno" holds the same view. " Welche Hoff- 
nung zur Philosophie fiir den, welcher sie in der Logik sucht ? Keine." 



INTRODUCTION. ll 

of Kant's system. The most eminent name among the 
strictly formal Logicians since Kant is Herbart ; but both 
he and his disciple Drobisch have pushed to an extreme 
Kant's error in an exclusively a priori view of the 
science. 

On the other hand, the Logic of Hegel reconstructs from Hegel. 
the opposite side the metaphysical fabric which Kant 
had overthrown. After the Kantian Critique, it was 
impossible to bring a philosophy of the Absolute 
within the received compass of Jiuman thought : there 
remained only the attempt to expand thought to the 
immensity of the object, by a gigantic scheme of Intel- 
lectual Pantheism, in which the personal consciousness 
and its limits should be absorbed in the processes of the 
one Infinite Mind. Such is the fundamental principle of 
the Logic of Hegel, a Logic constructed, not in obe- 
dience to, but in defiance of, the laws of thought, which 
are held to be valid only for the finite understanding 
dealing with finite objects; the philosophy of the infinite 
being based on their abrogation. 

It is not easy to give in a short compass an account 
of Hegel's Logic, which shall be intelligible to an English 
reader. If we were to describe it as an attempt to 
develope a Philosophy of Being in general, by repro- 
ducing the Divine Thought in the act of Creation, we 
might support the view by sufficient quotations from the 
work ; but it would convey an erroneous impression to 
one who did not bear in mind the total suppression of 
personality, divine as well as human, in the Hegelian 
philosophy. It may perhaps be better characterized as 
an illegitimate expansion of the fundamental principle 
of the Cartesian philosophy, modified in some degree by 
the Kantian. " Cogito, ergo sum" is true within the 
limits of the personal consciousness. I exist only in so far 
as I am conscious of my existence ; and I am conscious 



Hi INTRODUCTION. 

only as being affected in this or that determinate manner. 
Within these limits Thought and Being are identical, and 
every modification of the one is a modification of the other. 
But if the same principle is to be accepted in its Hegelian 
extent, 1 must commence by ascending from my per- 
sonal consciousness to a supposed Universal Thought, 
identical with Being in general. Here personality dis- 
appears altogether ; and the problem is, to deduce from 
the identity of Thought and Being in general, the several 
identical determinations of the one and the other. Such 
a process is not thought but its negation. If the Uni- 
verse had one consciousness, the system might be 
possible ; for Thought and Being are identical only in 
and through consciousness. But such universal con- 
sciousness could not be my consciousness ; and thus 
the Hegelian assumption cannot be grasped by any act 
of human thought. On the other hand, thought without 
consciousness is inconceivable ; since it implies a ne- 
gation of the one essential characteristic under which 
all thought is presented to the human mind. The logical 
notion which is not a function of my own personal 
thought, is a mere empty abstraction, inconceivable by 
reason; and the system deduced from it is incompatible 
with those regulative truths that are above reason. 
Vulgar Rationalism subjects belief to thought; it has 
been reserved for Transcendental Philosophy to subject 
it to the annihilation of thought. 

Speculative philosophy has had three great periods, 
each of which has been consummated by a critical 
system of which Formal Logic has been a constituent 
portion. The Eleatic and Platonic metaphysics found 
their consummation in Aristotle ; the Scholastic Philo- 
sophy in Occam; that of the seventeenth and eighteenth 
centuries in Kant. But from the Kantian philosophy 
has arisen another phase of speculation, not less dogmatic 



INTRODUCTION. liii 

in its positions, not less extravagant in its aims, not less 
unstable in its foundations. A criticism which shall sift 
thoroughly the pretensions of this philosophy, it remains 
for the present generation to accomplish. 



PART II. CRITICAL. 



" That Logic," says Kant, " has even from the earliest /<-'^-^< 
times advanced in the sure course of a science, is manifest ^^ ii^"' 



from the fact that since Aristotle it has taken no back- '^""-!Z— / 

ward step." " It is worthy of remark however," he con- ^^ ' ' 

tinues, " that it has also up to this time been able to 

take no step forward, and thus to al] appearance seems i 

to be concluded and perfected." This remark is true 

as regards what Aristotle did ; but on the other hand, as 

regards what Aristotle left undone, it is no less true that 

the whole subsequent history of the science exhibits 

scarcely any thing but the ebb and flow of unsettled 

opinion. The master left behind him a collection of 

writings; and to the substance of that collection his \ 

disciples have, for the most part, faithfully adhered ; 

but he left no definition of the science on which he 

wrote, and no principle for determining its boundaries ; 

and these accordingly have been matter of controversy 

ever since. 

Clitomachus compared the Logic of his day to the j^^^^--*-*^^**' 
moon, which never ceases waxing and waning". The ^^ €Z-^ /(^<^<r^ 
cause of complaint has assuredly not been diminished *^' ^ "^ ^^ 
by the labours of subsequent expositors down to the '^ Z^'"-^^--' 
present time. Few logicians have in their practical *^( 
treatment materially added to or taken from the original 

* KAejTOyuaxos ^Ik'x^'5 tV StaAeKTtK^j' t^ aeXiivp, Kal yap Tavrrju oil 
TtaiiaQai (pQivovaav koX av^ofxeurju. Stoheei Eel. Seim. Ixxx. 

e 



' .^fc. J'<^ 



liv INTRODUCTION. 

body of the system : few on the other hand are theore- 
tically agreed as to what it is that they are expounding. 
Ask of almost any writer, "What is Logic?" the reply 
is almost unanimous, that it is the subject treated of in 
Aristotle's Organon. Ask what is this subject; and 
nearly every commentator has a different definition. 
'S^y'^-^'^'^'T^.r.Let us bring together a few of these conflicting 
witnesses. Logic is a part of philosophy^. It is not 
a part, but an instrument^ It is both a science and an 
art**. It is neither science nor art, but an instrumental, 
habit". It is a science and not an art^ It is an art 
and not a science §. It is the science of argumentation^ — 
of the operations of the mind so far as they are dirigible 
by laws ^— of the syllogism^ — of the understanding in 
relation to evidence' — of the laws of thought"*. It is 
the art of thinking ° — of reasoning ° — of the right use of 
reason p — of dissertation *! — of teaching' — of directing the 
mind to any object' — of forming instruments for the 
direction of the mind*. 

^ The Stoics. See Ammonius, Prooem. in Categ. Philoponus, Procem. in 
Anal. Prior. 

c The Peripatetics. See Ammonius, Prooem- in Categ. Philop., Procem. 
in Anal. Prior. 

^ Petrus Hispanus, JEmilius Acerbus, Bentham, Kirwan, Whately, 
J. S. Mill. 

" The Greek Commentators, Zabarella, Smiglecius. 

*■ Alhertus Magnus, Aquinas, Scotus, Wolf, Kant. 

g Ramus, Keckermann, Bm-gersdyck, Sanderson, Aldrich. 

^ Alhertus Magnus, Alfarabi, A\icenna, Algazel. 

» Aquinas. 

k Scotus. 

1 J. S. MiU. 

^ Kant, Hoffbauer, Krug, Sir W. Hamilton. 

" Gassendi, Amauld. 

o Le Clerc, Crakanthorpe, Wallis, Kirwan, "VVhately. 

p Clauberg, Watts. 

n Eamus. 

>■ Melanchthon. 

' Bentham. 

t Burgersdyck, Sanderson, Aldrich. 



INTRODUCTION. Iv 

Let US endeavour to disentangle some of the confusion 
in which the reader may be involved by this multitude of 
definitions. Logic was divided by the Schoolmen into 
the Logica docens and the Logica uteris, and the same 
division had been made before by the Greek Com- 
mentators, under the title of Logic without and with 
application to things'". The former denotes Logic in its 
theoretical character, as concerned merely with the laws 
and forms of thought; the latter is the practical appli- 
cation of thought to this or that object matter. The 
discrepancies in the definition of Logic, as Science or 
Art, may partly be traced to a confusion between these 
two. 

The Logica docens is properly a Science and not an<^ u<-^^* c^c:^^^^ ^ 
Art. It is not correct to say, as has frequently been •^'-**^^ ' <^^^-^ 
said or implied by modern Logicians, that every Science 
is an Art, because all knowledge admits of a practical 
application. "The truth is," says Bentham, "that how- 
soever clearly distinguishable in idea, the two objects, 
Art and Science, in themselves are not, in any instance, 
found separate. In no place is any thing to he done, 
but in the same place there is something to he known; 
in no place is anj' thing to l)e known, but in the same 
place there is something to be done." The terms thus 
extended are too vague to be of any value, and tend to 

" " Intelligendum est tamen quod Logica dupliciter consideratur. Uno 
modo in quantum est docens, et sic ex necessariis et propriis principiis 
procedit ad necessarias conclusiones, et sic est scientia. Alio modo in 
quantum utimur ea applicando earn ad ilia in quibus est usus, et sic non 
est ex propriis, sed ex communibus ; nee sic est scientia." Scotus, super 
Univ Porph. Qu. 1. "Est Logica docens, quae tradit praecepta, quibus 
docetur quid, quomodo faciendum : utens vero est, quae ex praeceptis eflficit 
opera ipsis conformia, sicut cum artifex ex praeceptis artis eflficit opera 
artis." Smiglecii Logica, Disp. ii. Qu. vi. For the parallel distinction 
between Logic without and wdth application to things, (x^pis TrpayixdrMUy 
crvfifiifiaCofifurf ro7s irpdyixaaiv, iv xP'h^^'- ''"^ yvfxvacrla trpayfidTCDV,) see 
Ammonius, Prooem. in Categ. Philoponus, Prooom. in Anal. Prior. 

e 2 



Ivi INTRODUCTION. 

confuse rather than to distinguish. Science is not Art, 
though scientific knowledge may be the basis of artistic. 
A Science admits of a practical employment under 
certain conditions; but it does not become an Art until 
those conditions are complied with, and it may exist 
as a Science without them. The ordinary distinction 
between the man of theory and the man of practice is a 
proof of this. A man may have a scientific knowledge 
of music, and yet have no power of playing on any 
instrument. He may be acquainted with the principles 
of perspective, without any skill in the use of the pencil. 
He may know the mathematical principles of Optics, 
and yet be sadly at a loss if required to make a pair of 
spectacles. He may have studied the anatomy of the 
human frame, and yet be unable to perform a surgical 
operation. He may talk like a Curius, and live like a 
Bacchanal. And in like manner, he may be familiar 
with Barbara, Celarent, and Barali'pton, but in practice 
be a weak and inconclusive reasoner. On the other 
hand, he may possess Art without Science, that is to say, 
he may have considerable dexterity in the practice of 
any operation, without being able to give a clear account 
of the principles on which it is conducted. Science 
is no more Art because the man of science may become 
an artist, than a boy is a man because he may grow up 
into one. Nay, far less so; for the boy becomes a man in 
the course of nature, without any effort of his own ; while 
the man of theory may remain a man of theory all his 
life, without ever learning to apply his knowledge to 
practice. 
'^ /c^c<^?y/,^ When we are asked. What is Logic? it is clearly 

'/^-^^^f ^^^^--^^^QQ^^l^ What is the object of which books on Logic 
treat. No treatise on Logic can give all its practical 
applications. It can at best select only a few speci- 
mens, and these by way of example, not as an essential 



INTRODUCTION. Ivii 

part of the theory. But it professes to give, and is 
bound to give, the entire principles of reasoning, or 
rather of thinking in general, even though it illustrates 
its teaching by no other examples than algebraical 
symbols. A treatise on Logic is not designed primarily 
to give men facility in the practice of reasoning, any 
more than a treatise on Optics is intended to improve 
their sight ; and it would be as correct for a writer on 
the mathematical principles of Optics to entitle his work, 
Optics, or the art of improving defective vision," as it 
is for a writer on the principles of Logic to adopt for 
his title, " Logic, or the art of reasoning." Yet we do 
not therefore deny that a knowledge of Optics is useful 
in making spectacles, nor that a knowledge of Logic is 
valuable in the practice of reasoning. 

Art, in the strict sense of the term, is acquired by 
practice, Science by study". A man who has learnt to 
reason accurately by practice in special cases, without 
a knowledge of the laws of the syllogism, has the art of 
reasoning, but not the science. He who knows the 
theory, but does not practise it, has the science of 
reasoning, but not the art. The Logic to be found in 
treatises on the subject, i. e. the Logica docens^ is thus 
clearly a science and not an art ; for it is gained by 
study and not by exercise. But there is a further ^\^-, ^^ o^iZi.iUZ^ 
tinction between speculative and practical science, sJic d^<'/^f-^iZic. 
according as the knowledge which it conveys is con- ^^dJ^a^AA 



/ 



•"^ See Wolf, Philosophia Ratlonalis, Proleg . §. 10. " Omnis Logica utens 
est habitus, qui proprio exercitio comparatur, minima autem discendo 
acquiritur, adeoque at ipsa docai'i nequit. Quamobrem, cum Logica 
omnis sit vel docans vel utens, neque euim prsetar regularum notitiam 
atque habitum aas ad praxin transfarandi tertium concipi potest; sola 
Logica artificialis docans ea est qu*. doceri adeoque in numerum disci- 
plinarum philosophicarum referri potest. Atque ideo quoqua Logicam 
definivimus per sciantiam, minime autem per artem vel habitum in genera, 
quod genus convenit Logicse utenti." 



Iviii INTRODUCTION. 

sidered as an end in itself, or only as a means to be 
applied to some further purpose''. And here again, 
Logicians of eminence, who are agreed as to the genus 
of Logic, are at issue as to its species. Granted that 
Logic is a science, is it speculative or practical ? Wolf, 
the ablest of the German writers on Logic before Kant, 
while distinguishing accurately between Science and 
Art, regards Logic as belonging to the practical, not to 
the speculative sciences, the knowledge which it fur- 
nishes being subservient to the discipline of the mind 
' /^.t./^*--^^^ ^^^ ^^ acquisition of further truths. Accordingly 
fa.t^s'ua^ /fi^'^^^^^^Q defines Logic as " Scientia dirigendi facultatem cog- 
noscitivam in cognoscenda veritate^" On the other 
r^^^-T'^'^^^^ hand, Kant, who defines Logic as " the Science of the 
^e^Uc^^L^^^-^' necessary laws of the Understanding and the Reason," 
considers and treats it as speculative"*, and the same 
view is well maintained by the excellent French trans- 
lator of the Organon, M. St. Hilaire, whose language 
may be quoted as an accurate and admirably expressed 
statement of the true purpose of Logic and the spirit in 
which it should be studied. " Sans la logique, I'esprit 
de I'homme pent admirablement agir, admirablement 
raisonner; mais sans elle, il ne se connait pas tout 
entier : il ignore I'une de ses parties les plus belles et 
les plus fecondes. La logique la lui fait connaitre. Voila 
son utilite: elle ne pent pas en avoir d'autre^." 
, CZ<-^^^(^jr£y^-^ That this latter is the true view is manifest, as soon as 
y^^'v^^ we distinguish accurately between the essential con- 

• ,t:^L^eC.^^^t£^'aZl ^ Arist. Metaph. A minor, c. 1. 'OpOws S' ex^i Kcd rh KaK^lffOai t^v (piKo- 
<^< " ^ /fc^^ ■£^<^^^-'^^4ro(plav iirt.ffT'fiixTjv rrjs aXTjOeias, ©euprjTiKrjs fihv yhp Te\os oA^^eta, irpo/CTtKTjs 

„^,t^_/ ^ ,{^2^3=wX/ ^ Philosophia Rationalis, §.61. This was also the opinion of Occam and 
W, i^^'^ ^ ^^^^^Lt^thers. See -<Emilius Acerbus, Qusest. Log. Qu. v. 

-^.^ ol^ ' " Logik, Einleituny I. This was also the opinion of Scotus and others. 

See ^milius Acerbus, 1. c. 
^ Preface, p. 42. 



INTRODUCTION. lix 

tents of Logic and its accidental applications. The 
benefits performed by Logic as a medicine of the mind, 
however highly we may be disposed to rate them, are 
accidental only, and arise from causes external to the 
science itself; its speculative character, as an inquiry 
into the laws of thought, is internal and essential. To 
the twofold character of Logic, two conditions are neces- 
sary. Firstly, that there should exist certain mental 
laws to which every sound thinker is bound to conform. 
Secondly, that it should be possible to transgress those 
laws, or to think unsoundly. On the former of these 
conditions depends the possibility of Logic as a specu- 
lative science : on the latter^ its possibility as a practical 
science. Now if we look at these two conditions with 
reference to the actual contents of pure Logic, it is 
manifest that the abrogation of the first would utterly 
annihilate the whole science ; whereas the abrogation 
of the second would at most only necessitate the removal 
of a few excrescences, leaving the main body of logical 
doctrine substantially as it is at present. Suppose, for 
example, that the difference between sound and unsound 
reasoning could be discerned in individual cases as a 
matter of fact, but that we had no power of classifying the 
several instances of each and referring them to common 
principles. It is clear that under such a supposition, 
tiie present contents of Logic, speculative and practical, 
could have no existence. The number of sound and 
unsound thinkers in the world might remain much as 
it is now ; but the impossibility of investigating the 
principles of the one and applying them to the cor- 
rection of the other, would make a system of Logic 
unattainable. But let us imagine, on the other hand, 
a race of intelligent beings, subject to the same laws of 
thought as mankind, but incapable of transgressing them 
in practice. The elements of existing Logic, the Con- 



Ix INTRODUCTION. 

cept, the Judgment, the Syllogism, would remain 
unaltered. Logic, as a speculative science, would 
investigate the laws of unerring reason, as i^stronomy 
investigates the unvarying laws of the heavenly phe- 
nomena; but a practical science of Logic, to preserve 
the mind from error, would be as absurd as an Astronomy 
proposing to control and regulate the planets in their 
courses. From these considerations it follows that, 
even granting Logic to be, under existing circumstances, 
both a speculative and a practical science, yet the 
former is an essential, the latter an accidental feature ; 
the one is necessarily interwoven with the elements of 
the system, the other is a. contingent result of the 
infirmities of those who possess it. 
,tUx^..^ i..*^A^ Qjj ^Q other hand, the Logica utens may be either 
!12Cr.^X«^.c.-^ Science or Art, according to the purpose to which it is 
"'^^tifi^ '"applied c. Whenever reasonings are employed on any 
special object of knowledge, there we have an instance 
of the Logica utens. The opposite view, which is some- 
times ta,ken on account of Aristotle's distinction between 
the logical and the analytical or physical syllogism, 
arises from a confusion between the Aristotelian and 
the later senses of the term logical. 

It would be both tedious and unnecessary to discuss 
in detail the various accounts that have been given of 
the object of Logic, by those who are agreed as to its 
genus. Many of these may be passed over, as being 



^ " Distinctio peccat, quia auctores distinctionis vocant Logicam uten- 
tem solum usum partis Topicse, cum Logica utens vel conjuncta rebus 
potissimum dicatm-, et de aliis partibus Logicse rebus conjunctse numquid 
non poterunt applicari rebus ea quae de definition e et divisione demon- 
strationeque prsecepta traduntur ? Ex quo sequitur ut Logica utens sit 
quandoque vere Scientia, ut puta Pbysica vel Metaphysica, vel siqua 
alia est, pbysicus enim demonstrans mixtum ex elementis esse corruptibile 
est Logicus utens, et talis Pbysica est Logica utens et vere Scientia." 
Acerbl Quasi. Lo(j, Qu. IV. 



v^/ 



INTRODUCTION. Ixi 

merely verbal varieties of the same fundamental view^. 
One or two statements, however, require a brief notice, 
as having been maintained by eminent authors in recent 
times, and involving views which it is important to a 
clear understanding of the nature and legitimate con- 
tents of Logic to distinguish from each other. 

According to Archbishop Whately, Logic may be -^^^^ oiL,e^' u 
defined as the Science and Art of Reasoning^, In this a. J^^/j:?- /^ 
point of view, the processes of apprehension and judg- Lc^^fr, i^^^^^it^ 
ment are considered not in themselves as independent "t," • ^ 

acts of thought, but as subordinate to argumentation. ^ 

"This view," says Sir William Hamilton^, "which may 
be allowed in so far as it applies to the Logic contained 
in the Aristotelic treatises now extant, was held by 
several of the Arabian and Latin Schoolmen ; borrowed 
from them by the Oxford Crakanthorpe, it was adopted 
by Wallis ; and from Wallis it passed to Dr. Whately. 
But, as applied to Logic, in its own nature, this opinion 
has been long rejected, on grounds superfluously con- 



^ Thus the opinion of Aquinas is virtually identical with Kant's, and that 
of Scotus with Archhishop Whately's. 

e In another passage, Archbishop Whately maintains that Logic is ^«,yt^^y>^ *^^^-^ 
entirely conversant about languat/e ; adding, " If any process of reasoning pTa «-♦/ i^ ^a~t 



can take place in the mind, without any employment f language, orally 
or mentally, (a metaphysical question which I shall not here discuss,) 
such a process does not come within the province of the science here 
treated of." That language in its most extended sense, i. e. some system 
of signs, verbal or other, is essential not merely to the communication, 
but to the formation of thought, appears to be proved by universal expe- 
rience and by the character of conceptions as distinguished from in- 
tuitions. But notwithstanding this, language must be regarded only as 
the secondary and accidental object of Logic, which is primarily conversant 
about the laws of thought, not about the instrument by which it is formed 
or communicated. And if any process of human thought were possible 
without language, (which Archbishop Whately appears to consider as at 
least conceivably true,) the laws of such a process would, equally with any 
other, be matters of logical investigation. On the question of the relation 
of language to thought, see Prolegomena Logica, p. 15. 

<■ Edinhiirgh Review, No. 115, p. 206. reprinted in his Discussions, p. 135. 



y 



Ixii INTRODUCTION. 

elusive, by the immense majority even of the Peripatetic 
dialecticians ; and not a single reason has been alleged 
by Dr. Whately to induce us to waver in our belief, that 
the laws of thought ^ and not the laws of reasoning, con- 
stitute the adequate object of the science." 

" The error," continues Sir W. Hamilton, " would be 
of comparatively little consequence, did it not induce 
a perfunctory consideration of the laws of those faculties 
of thought; these being viewed as only subsidiary to 
the process of reasoning." Of the truth of this charge 
there can be no question. A student might read 
through nearly every one of the popular treatises on 
Logic, without finding the slightest hint of the fact, that 
in the processes of conception and judgment, as well as 
in that of reasoning, there is a distinction to be made 
between the form of the thought and the matter, the 
former being equally in all three processes accurately 
and completely determinable by logical rules ; the latter 
being equally in all three beyond the domain of the 
science. A thought may violate its own laws, and thus 
virtually destroy itself; or it may be perfectly consistent 
with itself, but at variance with the facts of experience. 
The result in the one case is a product logically ille- 
gitimate, or the unthinkable i in the other the empirically 
illegitimate, or unreal. 

In both cases alike the mind is supposed to be 
already in possession of the necessary data for thinking 
at all. Where there is a material deficiency in the 
conditions preliminary to an act of thought, we cannot 
be said to think logically or illogically; for we cannot 
attempt to think at all. Thus, if we are told to conceive 
objects which have never been presented in their 
proper experience, a colour for instance which we have 
never seen, or a scent which we have never smelt; or 
if we are required to form a judgment, other than iden- 



INTRODUCTION. Ixui 

tical, with less than two concepts, or a syllogism with 
less than two premises, we are in the position of a 
builder without materials, who can neither obey nor 
disobey the rules of architecture. In every art or 
science, in every inquiry speculative or practical, the 
existence of the objects of inquiry is presupposed. The 
astronomer is not required to create the heavens, nor 
the grammarian to supply rules of speech to the mute 
fishes, nor the logician to analyse the laws of thought 
where no act of thought can be attempted. 

Thought is representative ; its primary materials are /2 l^^czi^ c/<^ 
presentations, either of the external or the internal sense, r" '^^ '^f *' '^r 

In the product of any act of thought, it is necessary to ^^^»„.w^^ . 

distinguish between the matter and the forrfi. The 
former is all that is given out of and prior to the 
thinking act; the latter is all that is conveyed in and 
by the act itself". To conception are given attributes ; 
to judgment are given concepts ; to reasoning are given 
judgments. By the act of conceiving, the attributes are 
thought as representing one or more objects ; by the act 
of judging, the concepts are thought as related to one or 
more common objects; by the act of reasoning, the 
judgments are thought as necessitating another judgment 
as their consequence. 

The thinking process itself may also be distinguished ai'^'-^Uirt 
as material or formal. It is formal when the matter 7' 

given is sufficient for the completion of the product, 
without any other addition than what is communicated 
in the act of thought itself. It is material when the 
data are insufficient and the mind has consequently to 
go out of the thinking act to obtain additional materials. 
If, for example, having given to me the attributes A, B, C, 

8 Cf. Hoffbauer, Logik, §.11. " Materie des Denkens sind Vorstellungen, 
aus welchen Gedanken erzeugt werden konnen, und die Form des Denkens 
ist die Art und Weise, wie dieses geschieht." 



Ixiv INTRODUCTION. 

I can think those attributes as coexisting in an object, 
without appealing to experience to discover what objects 
actually possess them, this is formal conceiving. If, 
having given to me the concepts P and Q, I can pro- 
nounce "P is Q," or *'P is not Q," without a similar 
appeal, this is formal judging. If, having given to me 
the judgments " W is X," " Y is Z," I can elicit a con- 
clusion from them alone, this is formal reasoning. The 
term experience is here used in a wide sense, for all 
accidental knowledge, all that is not part and parcel of 
the thinking act itself. 
'^^^ca^-^lIi-j/C^- One condition of formal conceiving is, that the attri- 
'^c-^Cc^^ . ^ butes given must not contradict one another. There 
is no contradiction between the notions of a horse's 
body and a man's head. A centaur therefore is as 
■ conceivable as a man or a horse, whether such a 

creature exists in nature or not. But if we try to 
conceive a surface both black and white in the same 
portion, the attempt to individualize the attributes by 
applying them to an object shews at once their incom- 
patibility. Such a combination of attributes is incapable 
of representing any possible object. Hence we have a 
law of thought, or condition of logical possibility; namely, 
that whatever is contradictory is inconceivable. This 
is the well-known Principle of Contradiction, the most 
general expression of which is, " nothing can be A and 
not A," or "no object can be conceived under contra- 
dictory attributes." 
J;!:^l_f:7*'^ '^ Another law of thought may be derived from the fact 
J ' . that all thought is representative of possible objects of 

I intuition^. Hence, whatever limits our constitution im- 
poses a 'priori on the presentations of intuition, the same 
limits hold good of the representations of thought. Now 

^ On the meaning of the term intuition, as distinguished from thought, 
see below, p. 2, notes o and d. 



'i fit^^-i^ciCu^ m-'f*^ 



INTRODUCTION. Ixv 

intuition is possible only under the condition of limit- 
ation by differences. An object of intuition, as such, 
possesses definite characteristics, by Tvhich it is marked 
off and distinguished from all others : otherwise it would 
not be an object, but the universe of all objects. In 
the act of conception, therefore, when we regard certain 
given attributes as constituting an object, we conceive 
it as thereby limited and separated from all other 
objects, as being itself o^ndi nothing else. The indefinite 
ideas, therefore, corresponding to the general terms, 
Thing, Object, Being in general, are not concepts, as con- 
taining no distinctive attributes; and the general object 
denoted by such terms is inconceivable. This law of 
thought is expressed by the Principle of Identity, 
" Every A is A," or " Every object of thought is con- 
ceived as itself." 

Attributes which comply with these law^s are logicallynL Ci.^ f^/'^^ ^^ 
conceivable; but for an act of material conception, or ^ - ^/ 

rather of conception combined wdth perception or / / 
memory, more than this is required. A centaur, as has 
before been observed, is logically as conceivable as a 
horse ; and, as mere thoughts, one is as legitimate as the 
other. But the senses or other evidence must further 
assure me of the reality of the objects, before I can 
think of either horse or centaur as having any existence 
out of my imagination. This assurance is not the result 
of a law of thought, but of a fact of perception. Hence 
as a general rule : all imaginary objects are conceived 
as such formally ; all real objects are conceived as such 
materially, that is to say, not by an act of pure con- 
ception, but by uniting that act with the presence or 
remembrance of other sources of information. 

Formal judging is possible, affirmatively, whenever^w^^^^t^-^' 
one of the given concepts is contained in the other ;/^^^^^^;;2^ 
negatively, whenever one of them contradicts the other. u-iiUiXZ. 



Ixvi INTRODUCTION. 

If the concepts P and Q have no attributes in common 
or contradicting each other, I cannot determine whether 
they coexist in any object without an appeal to expe- 
rience ; but if Q contains the attributes O, P, I can by 
a law of thought alone determine that all Q is P, or if 
Q contain an attribute contradictory of P, I can in like 
manner determine that no Q is P. The Laws of Identity 
and Contradiction are here again called into operation. 
Hence as a general rule: all analytical judging is formal; 
all synthetical judging is material. 

Formal reasoning is possible when the given judgments 
are connected by a middle terra under such conditions 
of quantity and quality that the mere act of thought 
necessarily elicits the conclusion. If any addition to 
the data is required, the consequence is material. 
Purely formal mediate reasoning or syllogism is de- 
pendent on the same laws as formal judging, the Law 
of Identity governing the affirmative categorical syllo- 
gism and the Law of Contradiction the negative^; while 
J". ^ the subordinate Law of Excluded Middle is called into 

J; operation in the immediate inferences of Opposition 
and Conversion^ A single example must suffice. In 
a syllogism in Barbara we reason in this form. " All 
A is [some] B, all C is [some] A, therefore all C is 
[some] B." The law which determines the conclusion 
is, that whatever is identical with a portion of A is 
identical with a portion of that which is identical with 
all A. Here is again the Principle of Identity. "Every 
portion of a concept is identical with itself." The 
other forms of syllogism may easily be analysed in the 
same manner. 



" Hypothetical and Disjunctive judgments and reasonings are omitted, 
as being either extralogical or reducible to Categorical form. See this 
question discussed in the Appendix, Note I. 

J See Prolegomena Logica, p. 200. 



INTRODUCTION. Ixvii 

The critical province of Logic is coextensive with the v^*^ /^HceJ^ 
constructive. As the logician can form concepts, judg- f"^ 
ments, reasonings, in a certain manner from certain 
data, so he is competent to examine all that is or pro- 
fesses to be formed in like manner from like data. To 
distinguish the apparent from the real is the purpose 
of logical criticism "": that which presents no false ap- 
pearance is beyond its field. If a thought professes to 
be based solely on formal grounds, to be guaranteed 
as legitimate by the laws of thought alone. Logic is 
competent to examine and decide upon its pretensions. 
If it professes to rest in any degree on extralogical 
foundations, on a sensible experience for example, or on 
suppressed premises. Logic neither accepts nor rejects 
its claims to a material validity, but dismisses it to be 
tried before another tribunal. Accordingly, when Logic 
is defined to be the science of the laws of formal thinking, 
or the science of the laws of thought as thought, (not as 
modified by experience,) it follows that it can adequately 
determine the cone eiv ability of an object, the truth or 
falsehood of an analytical judgment, or the validity of 
Q> professedly formal reo^^onmg, in which the given premises 
are stated as the complete conditions of the conclusion. 
On the other hand, it cannot determine the real existence 
of an object, the truth or falsehood of a synthetical judg- 
ment, or the validity of a reasoning professedly material, 
in which the premises are given as a part only of the 
conditions of the conclusion. Formal thinking can be 
called into operation by itself. Material thinking can 
only operate in conjunction with an act of perception or 
memory J and the laws of thought alone are no guarantee 

^ Arist. Soph. Elench. c. 11. 'H 70^ ireipaaTiKri icrri SiaKcKTiKT} ris koI 
dewpel oil Thv elSdra aWa rhv ayvoovvra koX irpocriroiovfxeuou. 'O ixeu oZv 
Karh rh irpayfjLa d^wpcov to Koiua 5ia\e/CTtKds, 6 Se tovto tpaiyofxevus iroiwu 

(T0(f>l(rTlK6s. 



Ixviii INTRODUCTION. 

for the trustworthiness of the concomitant process. It 
is of course open to any innovator to attempt to extend 
the boundaries of the science by material additions ; but 
he does so in the teeth of Kant's demonstration, that a 
criterion of material truth is not only impossible, but 
self-contradictory. In attempting to enlarge the field 
of Logic, he only makes it impossible to assign to it 
any definite field whatever. If a single intruder is 
admitted from the province of material knowledge, no 
barrier can be devised which shall not with equal facility 
• A S^^^ access to all. 
e/--^^:Ca^^/. ^"^ ^^^ grouud objcctious may be taken against the 
^lu<f /.z^^x^-^view of another eminent English writer on Logic, whose 
Z^X^f^J^^^^*^ work has attained to a high and in many respects a well- 
^^^^^ , deserved reputation. According to Mr. Mill, Logic may 
be defined as " the science of the operations of the un- 
derstanding which are subservient to the estimation of 
evidence : both the process itself of proceeding from 
known truths to unknown, and all intellectual operations 
auxiliary to thisK" In accordance with this definition, 
his treatise on Logic is based on a combination of the 
Old and the New Organon ; and the Baconian rules for 
the interrogation and interpretation of nature are com- 
bined with the Aristotelian principles of the syllogism, 
as part and parcel of the same science. 

This definition appears as much too wide as that of 
Archbishop Whately is too narrow. The latter is open 
to objection, because it excludes from the province of 
Logic processes of thought dependent upon precisely 
the same laws, and subject to the same method of 
discovery and criticism, as that of reasoning. The 
present definition is open to objection, because it in- 
cludes within the province of Logic processes governed 
by different laws, involving fundamentally diff"erent me- 
1 Mill's Logic, vol. i. p. 13. 



INTRODUCTION. Ixix 

thods, and implying essentially distinct conceptions, 
united and confused by the ambiguities of a common 
language. 

In the first place : the purpose of the Aristotelian ^ ^>^s^-«^^^^fe^ 
Logic is to investigate the laws under which the subject ^^^ifif'--^ 4--^-^^ / 
thinks; the purpose of the Baconian Logic is to inves-^V*^ cr&y^C'^, ^( 
tigate the laws under which the phenomena of the object f~^ ^ ^ ^^:a^^ 
take place"". They are thus respectively occupied with *- i^«^'^<«^'^<^'^/ * 
the two opposite poles of human knowledge, the ego and ^^^//^^2T^ ^ 
the non ego. The questions of the former are to be an- ^^^.,^,^.*>^V^^ ^ 
swered by an examination of the internal consciousness ; Ce^^^i^*>--^-€j- ^ ch 
the questions of the latter by an examination of external ^^'^^"''^ /^/^ 
nature. The two systems are thus diametrically opposed y^ ''^^^j/*^'^^'^' .. 
to each other in their objects. In the second place : the^^^ '"^ ' 

Aristotelian laws are laws of thought as it ought to he, . ^ ^<.^<^ 
The Baconian laws are laws of nature as it is, Thev- ^cr-^.>^ > 
former are principles resting upon their own evidence ;/j-'^^--/^-«^^. 
certain ct priori as laws, whether actually complied with or 
not; approving themselves to consciousness the instant 
they are enunciated; and irreversible in thought, because 
thought itself is under their control. The latter are laws 
resting upon the evidence of the facts to which they relate ; 
valid only in so far as they are actually complied with ; 
and ceasing to be laws at all, the instant that an ex- 
ception to them is discovered. And, however universally 
true in nature, they are always reversible in thought; 
for prior to their discovery we had no reason to think of 
them at all, and afterwards we have only to discard an 
adventitious knowledge. The two systems are thus dis- 
tinct in their evidence; the opposite of the one being the 
mentally inconceivable, that of the other the physically 
impossible. In the third place: in the applications of the 
Aristotelian Logic we proceed from the law to the facts, 
constructing types of reasoning according to given prin- 

™ See Sir W. Hamilton, Beid's Works, p. 712. 
f 



IXX INTRODUCTION. 

eiples, and accepting or rejecting all actual cases, ac- 
cording as they do or do not exemplify the law. In the 
applications of the Baconian Logic we proceed from the 
facts to the law, accepting as genuine all that actually 
occurs, and rejecting every law that does not account 
for the facts. The two systems are thus opposed in 
their methods. 
'Cc^<^i^ /- 1^. e^^ On account of these differences, the fundamental 
z»^ c^yjiJ^rtT^^po^^^P^^o^^ of the two systems cannot be expressed 
gxi:_<,, /t. 6fc„ i^ tjie same terms without ambiguity. Law in the 
: .,_^.^ «*^ ^^^^r'^^Aristotelian system implies a consciousness of obli- 
^^^^^ /^^j^5^-^^^:gation, which exists whether realised or not in practice. 
'■ Law in the Baconian system means an uniform se- 

^ quence, which exists only as it is realised in practice. 

In the field of nature, the conceptions of cause and effect 
imply no more than the antecedent and consequent phe- 
nomenon. In the field of thought, the cause is the con- 
sciously productive self, the effects, the thoughts which 
by its own power and under its own laws it produces. 
Necessity in the one case denotes what invariably is ; in 
the other, what cannot but be thought. In short, there 
is hardly a term in the one which can be transferred to 
the other, except by analogy. In all that is phenomenal, 
the facts of the philosophy of matter can only be applied 
by imperfect analogy to the philosophy of mind. In all 
that is real, the facts of the philosophy of mind can only 
by imperfect analogy be made use of in the philosophy 
of matter. The Aristotelian Logic, like Mathematics 
and Moral Philosophy, is constructed a priori from con- 
ceptions; and its principles and conclusions are pri- 
marily true of the conceptions, secondarily only of actual 
objects, on the supposition that they conform to the 
conceived model. The type of perfect reasoning is the 
same, though there may not be such a thing as a perfect 
reasoner in the world ; just as the standard of morality 



INTRODUCTION. Ixxi 

is the same, though no man is morally perfect, and as 
the demonstrations of Geometry hold good of conceived 
figures, though such figures in their mathematical exact- 
ness are never met with in practice. On the other hand, 
the Baconian Logic, like the subordinate branches of 
physical science, is constructed a posteriori from the 
observed uniformities of nature ; and its principles and 
conclusions are true primarily of the facts as they exist 
in nature, secondarily only of our conceptions, so far as 
they are accurate representations of the facts. Hence the 
truth of the system entirely depends on the real exist- 
ence of the objects of which it treats ; and the whole 
fabric would fall to the ground if the objects were anni- 
hilated or their constitution reversed. Hence too, a 
conception not in accordance with facts is worse than 
useless : if it is not the representation of nature as it is, 
it cannot claim to be accepted as the representation of 
nature as it should be. 

An error of this sort becomes serious in its con-7yi< c^ "' < i^v^^ 
sequences. It is a great mistake to treat various defi- ^^ <^ * r/^^ c^ 
nitions of Logic as mere matters of opinion, in which'T^^ ,^02.-^ 
each person is at liberty to expand or contract the f^i^^ /^a^e^ 
boundaries of the science according to his own leading 
conception. The whole province of the practice of 
reasoning may be affected by an error in its theory. For 
example. A writer who treats the Organon of Aristotle 
and the Organon of Bacon as parts of the same system 
is in consistency obliged to regard the so-called laws 
of thought as being in reality laws of external nature"; 

n Thus Mr. Mill {Logic, vol. i. p. 235.) obsenes : " So long as what 
were termed Universals were regarded as a peculiar kind of substances, 
having an objective existence distinct fiom the individual objects classed 
under them, the dictum de omni conveyed an important meaning ; because 
it expressed the intercommunity of nature, which it was necessary upon 
that theory that we should suppose to exist between those general sub- 
stances and the particular substances which were subordinated to them. 



JXXII INTRODUCTION. 

and the same obligation extends to all cognate branches 
of knowledge. Hence the laws of physical causation 
are introduced without modification into the moral and 
intellectual world ; and, instead of an ideal science of 
man as he ought to think or act, we are presented with 
an empirical science of the observed relations between 
thoughts or actions as they actually take place. Thus in 
the place of a system of Ethics based upon the theory of 
a free will as it ought to be determined by moral obli- 
gations, is substituted Ethology, or the science of the 
actual phenomena of habits formed by a necessary agent 
under the laws of an invariable causation °. And in con- 
sistency, as a part of the same system, we ought also to 
be presented with an a posteriori science of Geometry, 
based upon the measurement of figured bodies as 
actually found in nature. This alone is needed to 
furnish the consummation, and at the same time the 
reductio ad absurdum, of the whole system?. 



That every thing predicable of the universal was predicahle of the various 
individuals contained under it, was then no identical proposition, but a 
statement of what was conceived as a fundamental law of the universe." 

o The reader need scarcely be reminded, that this is Mr. Mill's actual 
conception of Ethology as the Exact Science of Human Nature. See his 
Logic, B. VI. Chap. V. 

P This indeed is almost implied in the conception of M. Comte, who 
regards it as the principal office of Mathematics to furnish a substitute 
for the measuring rod. To quote his own words. " Nous devons regarder 
comme suffisamment constatee rimpossibilite de determiner, en les me- 
surant directement, la plupart des grandeurs que nous desirous connaitre. 
C'est ce fait general qui necessite la formation de la science mathematique. 
Car, renongant, dans presque tous les cas, a la mesm^e immediate des 
grandeurs, I'esprit humain a du chercher a les determiner indii'ectement, 
et c'est ainsi qu'il a ete conduit a la creation des mathematiques." 
Oours de Philosophie Positive, t. i. p. 123. With this may be contrasted 
the language of Plato, Rep, vii. p. 527. Aeyovffi [xiv irov /xdXa yeXoias re 
Kol auayKaiws' ws yap irpaTTOvres re Kal irpd^ews 'ducKa irduras rovs \6yous 
■7roiovfj.evoi Xeyovcrii rerpaywvi^eiv re koI irapareCveip Kal Trpo(rTideuai, Kal 
Tavra ovtcc (pB eyy 6 fievoi' rb S' eCTt ttov irav rh fidOrf/xa yucixreais %veKa eirmr)- 
SevS/xei/ou. 



INTRODUCTION. Ixxiii 

On the above grounds, we are justified in rejecting 
Mr. Mill's definition of Logic as too wide for scientific 
accuracy, as that of Archbishop Whately is too narrow 
for scientific completeness. Between these two, the 
views of Kant, which have been substantially adopted in 
the preceding pages, hold an intermediate position, and 
one which promises more effectually than either to secure 
for the science what it has long needed, an exact de- 
finition and a systematic treatment. In accordance 
with these views, the conception of Logic which has 
been taken as the basis of the present work is that of 
the Science of the Laws of Pure or Formal Thinking, or, 
in thejlanguage of Sir William Hamilton % "the Science 
of the Laws of Thought as Thought." 

q Reid's Works, p. 698. 



9ir^ 



ARTIS LOGICS 



RUDIMENTA. 



I 



ARTIS LOGICS 

RUDIMENTA. 



CAP. I. 
De Terminis Simplicibus, 

§. 1. Mentis operationes in universum tres 
sunt*. 1. Simplex Apprehensio. 2. Judicium, 
3. Discursus^. 

^ Mentis operationes tres sunt. More correctly : the products 
of pure thought are three, the Concept, the Judgment, and 
the Syllogism. Whether these are to be referred to three 
distinct operations of mind, is a psychological, not a logical 
question. At any rate, the three operations must be regarded 
as a merely logical division, invented as a convenient mode 
of classifying the products of thought, which are the proper 
objects of Logic. Cf. Herbart, Psychologie als Wissenschaft, 
Th. ii. §. 119. 

^ " Sicut dicit Philosophus in tertio de Anima, duplex est 
operatio intellectus, Una quidem, quae dicitur indivisibilium 
intelligentia, per quam scilicet apprehendit essentiam unius- 
cujusque rei in se ipsa. Alia est operatio intellectus, scilicet 
componentis et dividentis. Additur autem et tertia operatio, 
scilicet ratiocinandi, secundum quod ratio procedit a notis ad 
inquisitionem ignotorum. Harum autem operationum prima 
ordinatur ad secundam : quia non potest esse compositio et 

B 



Z ARTIS LOGICS 

1. Simplex Apprehensio, est nudus rei con- 
ceptus intellectivus ''^ similis quodammodo per- 
ceptioni sensitivse '^ ; sicut enim Imago rei est in 

divisio, nisi simplicium apprehensorum. Secunda vero ordi- 
natur ad tertiam : quia videlicet oportet quod ex aliquo vero 
cognito, cui intellectus assentiat, procedatur ad certitudinem 
accipiendam de aliquibus ignotis. Cum autem Logica dicatur 
rationalis scientia, necesse est quod ejus consideratio versetur 
circa ea, quae pertinent ad tres prsedictas operationes rationis." 
Aquinas in Periherm. Lect. 1. Cf. Opusc. xlviii. Tract, de Syll. 
cap. 1. The passage alluded to by Aquinas is De An. iii. 6. 1. 
Tj fxev ovv tS)V dbiaipercov vo-qaris iv tovtois iv€p\ a ovk eari to yj/ev8os' iv 
ois de TO yj/'evbos Koi to d\r}6€s, crvvdeaLS tls rjdr] vor]fj.a.T(ov cocTrep iv 

ovTcov. 'AbialpeTa are either dpiBpS) or eiSet. Metaph. ix. 1. 4. 
The latter only are vorjTa, the former alo-di]Td. Cf. Anal. Post. i. 
24. 11. 

<= Simple Apprehension, in the only sense in which it can 
have any connection with Logic, is an operation of Thought, 
and is more properly called Conception. It is necessary to 
distinguish Thought, which is representative, and whose 
immediate object is an universal notion, gained by comparison 
and indifferently applicable to many individuals, from the 
various intuitive faculties, which are presentative, and whose 
immediate object is an individual thing, act, or state of mind, 
existing without or within ourselves. This distinction is 
properly psychological, but must be carefully borne in mind 
in reference to the logical character of Thought. A fuller 
explanation is given in Prolegomena Logica, Chap. I. 

^ Among various intuitive faculties, it is necessary to dis- 
tinguish between Sensation, Perception, and Imagination. The 
two former are distinguished by Stewart, Outlines of Moral 
Philosophy, §. 15. " Sensation expresses merely that change 
in the state of the mind which is produced by an impression 
upon an organ of sense ; of which change we can conceive the 
mind to be conscious without any knowledge of external 
objects. The word Perception expresses the knowledge we 
obtain, by means of our sensations, of the qualities of matter." # 



RUDIMENTA. d 

oculo, ita Idea in animo ^ : estque Incomplexa vel 
Complexa, 

Apprehensio simplex Incomplexa, est unius ob- 
jecti, ut calami, vel etiam plurium, confuse ; ut 
calami, manus, &c. Complexa, plurium, sed cum 
ordine quodam et respectu ; ut calami in manu\ 

And so M. Royer Collard, Jouffroy's Reid, vol. iii. p. 329. " II 
y a dans I'operation du toucher sensation et perception tout 
ensemble : changement d etat ou modification interieure, 
c'est la sensation : connaissance d'un objet exterieur, c'est la 
perception." This distinction originated with Eeid : by 
earlier writers Perception was used Avidely, as coextensive 
with Consciousness in general. See Hamilton's Reid, p. 870. 
Imagination is properly the consciousness of an image in the 
mind resembling an absent object of intuition. The image, 
like the object which it represents, is individual. By the 
earlier writers, logical and psychological, this and other pro- 
cesses of intuition are confounded with those of thought. 
Thus Gassendi, from w^hom Aldrich has borrowed, treats 
Imagiiiation, Simple Apprehension, Conception, Notion, and 
Intellection, as identical, and employed in the formation of 
images, ideas, concejjts, or phantasms of things. 

e Idea. In the later and post-Cartesian sense of the word; 
in which sense, it is defined by Locke, " whatsoever is the 
object of the understanding, when a man thinks." For the 
history of this word, see Sir W. Hamilton, Edinburgh Review, 
No. 99. p. 18-2. 

^ Confuse. This confuted apprehension of many objects is 
in truth only a succession of single apprehensions : thus in the 
example, we have two apprehensions, first of calami, and then 
of manus. Aldrich's distinction between incomplex and com- 
plex Apprehension is inaccurate, and depends merely on an 
accident of language. In respect of thought, it is indifferent 
whether we express the same notion in many words, as an 
animal with the head of a man and the body of a horse, or in one 
word, as Centaur. Complex Apprehension should properly 

b2 



4 ARTIS LOGICS 

2. Judicium, est quo mens non solum percipit 

duo objecta, sed, quasi pro tribunal! sedens, ex- 

presse apud se pronuntiat, ilia inter se convenire 

aut dissidere^ 

Arist. de Est enim Judicium aliud Affirmativum, quod 

Int. i. 3. 

vocatur etiam Compositio^ ; aliud Negativum, quod 
et Divisio, 

Porro, tam particula Est, quae affirmando con- 
venientiam exprimit^ quam Non-Est, quae negando 
Dissidium, appellatur Copula; (sicut et Gram- 
matica Conjunctiones Disjunctivas habet ;) at que 
hanc sub determinatione cognoscendo differt Judi- 
cium ab Apprehensione complexa. 

E. g. Si quis dixerit Triangulum cequilaterum 

be applied only to the apprehension of the proposition, (the 
\ oratio perfecta, — Aquinas, Opusc. xlviii. de Int. c. 3.) as dis- 
tinguished from that of a term or an imperfect sentence. 

e Percipit duo ohjecta. This expression is only accurate in 
the earlier and wider sense of perceives = is conscious of. The 
elements united in the logical judgment proper are general 
notions, the objects of Conception. With this explanation, 
Aldrich's definition is tolerably accurate as regards the 
logical judgment, formed by the union of two concepts repre- 
sented each by its separate sign in language. But this must 
not be confounded with the psychological judgment, which 
takes place in every act of consciousness. The latter is a 
conviction of the presence of the object of consciousness, 
either internally in the mind or externally in space. This | 
judgment does not require the aid of language, and to it.' 
Aldrich's definition is not applicable. Cf. Cousin, Cours de 
Philosophie, le9on 23. Hamilton on Eeid, p. 243, 375. 
Prolegomena Logica, p. 53. 

^ Compositio— (ru»/^eo-ty. Divisio — biaipca-is. See de Int. i. 3. i 



RUDIMENTA. O 

esse cBquiangulmn, possum Apprehensione Simplici 
incomplexa intelligere quid sibi velint singula 
Orationis hujus vocabula^ complexa vero quid tota 
sibi velit Oratio': Quin et ipsius Naturae \\\mme^ .Ai^ ^/n^ ^/^ 
intelligo. Duo quaelibet objecta vel inter se con-^^^*^ ^^^-^ 
venire, vel non convenire, et proinde altera Copu- 
larum esse jungenda : Nondum tamen feci judi- 
cium donee Copulam determinaverim, i. e. apud 
meipsum statu erim haec Duo Objecta, Triangulum 
cequilaterum, et Triangulum ceqiiianguliim, hac 
Copula Est, non autem altera Non-Est, oportere 
conjungi. 

3. Discursus^, est motus sive progressus mentis 

' Conception, the Apprehension of Logic, implies consi- 
derably more than the mere understanding of the meaning 
of words or sentences. A word or sentence may be intel- 
ligible when the notion signified is inconceivable. Conception 
consists in an uniUj of representation, i. e. in the power of 
forming a mental image of the several attributes given in any ' 
word or combination of words. It is thus imagination 
relatively to a concept. Cf. Hamilton on Reid, p. 377. Pro- 
legomena Logica, p. 24. 

J Ipsius Natur(e lumine. This so-called U()ht of nature is in 
truth one of the laws of thought, commonly known as the 
Principle of Excluded Middle. {Frincipium exclusi medii inter 
duo contradictoria.) 

^ " Additur tertia operatio qure est discursus, ab uno com- 
posite vel diviso ad aliud : hoc tamen fit per argumenta- 
tionem. Est autem argumentatio oratio significativa discursus 
rationis ab uno cognito ad aliud incognitum, vel a magis 
cognito ad minus cognitum. Sunt autem argumentationis 
quatuor species, scilicet syllogismus, enthymema, inductio, et 
exemplum." Aquinas, Opusc. xlviii. Tract, de Syll. cap. 1. 
The definition is too wide, being applicable to the immediate 



6 ARTIS LOGICS 

ab uno Judicio ad aliud ; quod et Ratiocinium 
dicitur; et significatur Copula Illativa, qualis est 
Ergo, aut alia similis. v. g. Qui est extra fortunce 
potestatem est beatus. Sapiens est extra fortunce 
potestatem. Ergo, Sapiens est beatus. 

Singulis operationibus sui accidunt defectus^ 

inferences of Opposition and Conversion, as well as to the 
mediate by Argumentation. In all there is a progress from 
one judgment to another. Disciirsus is more properly the 
progress from two connected judgments, to a third resulting 
from their connection. Cf. Port Eoyal Logic, In trod. " On 
appelle raisonner Taction de notre esprit, par laquelle il forme 
un jugement de plusieurs autres," 

Of this division of the operations of the mind, Sir W. 
Hamilton has observed, that " it never was proposed as a 
psychological distribution of the cognitive faculties in general : 
but only as a logical distribution of that section of them 
which we denominate discursive, as those alone which are 
proximately concerned in the process of reasoning." Reid's 
Works, p. 242, 692. Hence Aristotle's division, which is 
psychological, w^ll not exactly correspond. The nearest ap- 
proach to Simple Al^prehension is ri rav dBimperav vorjais; 
but vorja-ts is variously used, and in its widest sense will 
embrace all the logical operations, and even cpavraala, which 
belongs rather to the perceptive soul. See de Anima, iii. 
3. 8. Judgment will correspond nearly to the vwoXrjyj/is of de 
An. iii. 3. 7. (Cf. Trendelenburg Arist. de Anima, p. 469.) 
The latter term however is inapplicable to the cognition of 
axiomatic truths. Discursus answers to didvoia and XoyLo-fMos, 
the former term being applied both to the faculty and its 
operation. But there is much uncertainty in the use of all 
the above terms, Cf. Biese, vol. i. p. 89, 327. Hamilton's 
Eeid, p. 768. 

1 The service supposed to be performed by Logic in 
relation to these three defects is more fully and clearly stated 
by Burgersdyck Inst. Log. 1. ii. c. 1. "Mens nostra qua- 



RUDIMENTA. 7 

Apprehensioni, Indistinctio ; Judicio^ Falsitas ; 
Discursui, Mendosa Collectio, Quae cum Sapi- 
entes animadverterent, et opportuna illis remedia 
excogitassent, prsecepta sua in unum compegere ; 

druplici defectu laborat, cum occupata est in investiganda 
rerum cognitione : vel enim non assequitur propositae rei 
essentiam, sed circa illius accidentia solum hseret ac sensi- 
biles notas; vel essentiam rei confuse tantum concipit, et 
ratione minime distincta ; vel in dubiis non reperit quid 
statuat, aut etiam statuit quod falsum est; vel denique non 
servat ordinem in commentando, qui cum natura rerum 
consentit. Hisce quatuor malis opponit Logica totidem 
remedia. Definitio exhibet menti essentiam rerum : divisio 
efficit cognitionem distinctam : syllogismus tollit animi 
incertitudinem et errorem circa themata complexa: methodus 
ara^lav sive confusionem." Hence it appears that falsity of 
judgment simply was not regarded as remediable by Logic, 
but only falsity in relation to the syllogism, i. e. so far as it 
depends on the assumed truth or falsity of other judgments. 
But the above statement requires considerable limitation. 
Every process of thought is liable to a formal defect, as 
violating its own laws, and to a material defect, as inconsistent 
with experience. Thus a concept may be obscure or indis- 
tinct formally, as implying attributes which cannot be thought 
in conjunction, as when its different parts contradict one 
another: a judgment may be formally false, for the same 
reason : and a reasoning may be formally inconsequent, as 
transgressing the laws of the syllogism. In all these cases 
the fault may be detected by Logic. On the other hand, a 
concept may be materially obscure or indistinct, as containing 
attributes which we have never met with in our own expe- 
rience : a judgment may be materially false, as being at 
variance with facts : a reasoning may be materially incon- 
sequent, as not warranted by the laws or analogies of nature. 
Li all these cases, the fault can only be detected and reme- 
died by experience. Cf. Prolegomena Logica, p. 238. 



8 ARTIS LOGICS 

eorumque Scientiam dixere Logicam, sive Artem 
Rationis'^. 

Est igitur Logica, Ars instrumentalis dirigens 
mentem in cognitione rerum° : ej usque partes tres 

*^ Logicam. " Logica dicta est dno rov \6yov. Aoyos duplex 
est Aristoteli, 6 ea-a koX 6 e|a) X6yo9, id est, sermo internus et 
externus. Sermonem internum vocat t6v iv rfj yj/vxTj \6yop, id 
est, sermonem qui in anima est: Plutarchus, Damascenus, 
aliique appellant \6yov ivbidderov id est sermonem intus con- 
ceptum ; et externum, \6yov rrpofpopiKov, id est, sermonem foras 
prolatum, sive pronunciatum. Aoyos ivdidderos sive internus, 
nihil est aliud quam ratio sive cogitatio, hoc est, actio mentis 
res objectas earumque nomina concipientis. Mens enim non 
solum res ipsas concipit atque intelligit, sed et idonea vocabula 
excogitat ad conceptus suos aliis indicandos atque expHcandos : 
atque ita quodammodo in seipsa loquitur. Ao'yos- irpot^opiKos 
atque externus, est sermonis interni cogitationumque interpres, 
atque (ut Damascenus loquitur, lib. 2. de Orth. fid. cap. 21.) 
ayyekos rov vorjuaros, id est, nuiicius cogitationis. Ab utroque 
sermone appellata est Logica, (utrumque enim regit ac 
format) sed ab interno, quem nihil aliud esse diximus quam 
mentis rationem sive cogitationem, praecipue nuncupatur; 
f jf^- ab externo sermone, sive ab oratione, tantum secundario. 
Ij«.#^t** ' ^pliogica enim regit cogitationes animi nostri per se; orationem 
non per se, (hoc enim Grammaticse convenit) sed eatenus 
tantum, quatenus rationis nostrae sive cogitationum interpres 
est." Burgersdicii Inst. Log. 1. i. c. 1. Cf. Arist. Anal. Post. 
I. 10. 6. Ov Trpbs Tov €^ci) \6yov rj dnodeL^is, dXkd. rrpos top iv rfj "^vXTly 
inel ov8e (rvWoyiapos. 'Aei yap earLV evo-rrjvaL irpos rov e^co \6yov, dWd 
npos rov ecra \6yov ovk dei. 

^ Est igitur Logica. This definition is more fully given by 
Burgersdyck, List. Log. 1. i. c. 1. ''Logica est ars conficiens 
instrumenta, Usque intellectum dirigens in cognitione rerum. Logica 
docens dicitur quae prsecepta tradit ; utens, qu£e prseceptis 
utitur. Officium Logicae docentis, est tradere prsecepta et 
Kiodum efficiendi instrumenta, quibus mens dirigitur in cog- 



RUDIMENTA. y 

sunt, pro operation ibus mentis quas dirigit. 1. De 
Simplici Apprehensione, 2. De Judicio. 3. De 
Discursii, 

§. 2. QuoNiAM vero, inter docendum et dispu- 
tandum, neque res aliqua, neque conceptus, cui 
subjacet, commode in medium afferri potest ; ne- 
cesse est vicaria utriusque signa substituere, quorum 



nitione rerum, instrumentorumqiie naturam describere. In- 
strumenta Logica sunt quatuor, definitio, divisio, syllogismus 
et methodus. Officium Logicas utentis, est instrumenta, cum 
opus est, efficere, iisque mentem dirigere, ne in quserenda 
rerum cognitione hallucinetur." From this it appears that 
the knowledfje of things was regarded by this school as only 
the remote object of the Logica utens, as applied to this or 
that matter, and hence not to be gained from any logical 
treatise. Thus the distinction insisted upon by some critics 
between in cognitione and in cognitionem, is of no value ; both 
being merely verbal variations in expressing the same view. 
This definition of Logic as an art arose from the dialec- 
tical and rhetorical innovations introduced by tlie reformers 
of Logic in the latter part of the fifteenth century, and was 
adopted universally by Ramus and his followers, as well as 
by the Peripatetico-Ramists of the school of Keckermann, 
and afterwards by the Cartesians. Among the earlier philo- 
sophers, the Peripatetics considered Logic to be neither art 
nor science, but an instrument. The Stoics regarded it as a 
science, in which they were followed by the Schoolmen. 
Subsequently, in the schools of Wolf and Kant, Logic again 
obtained the name of Science, though the former regarded it 
as a practical, the latter, more correctly, as a speculative 
science. Cf. Zabarella de Natura Logicce, lib. i. Smiglecii 
Logica, Disp. 11. Qu. V. Sir W. Hamilton, Edinburgh Review, 
No. 115, p. 203. 



10 ARTIS LOGICS 

usum idbneum docendo, Logica mentem una ad 
bene operandum instruit. 

Hujusmodi signa apud homines recepta, sunt 

Voces: Nam Vox est signum rei vel conceptus" 

Deint.i.s. ex iustituto vicariumP*. et in significando^ primo 

quidem declarat conceptum, deinde supponit pro 

Ye\ Dico autem ex instituto, quia soni inarticu- 

° Primarily of the conception, secondarily of the thing. Cf. 
de Int. i. 2. Kal wanep ovbe ypafx^ara nao-t to. avra, ovbk (pavai al 
avrai- hv jxevroL ravra (Tr)p.eia 7rpa)T(os ravra ivacn TraBrjjiaTa rrjs "^X^^f 
Koi hv ravra o^oLOiiiaraf irpayfiara fjbrj ravra. On the distinction 

between ar)p,eiov and Sp-olcopa, see Waitz, vol. i. p. 3'24. 

^ ^^^^at Aldrich calls simply Vox, is called by Aristotle (fxovri 
a-rjfiavrLKT], and by Boethius and Petrus Hispanus, Vox signlficativa 
ad placitum. In the latter case, Vox is extended to the gram- 
matical word ; in the former, it is limited to what may be called 
the Vox Logica. Logic differs from Grammar, in considering 
language simply as the interpretation of thought, (the ipfirjveia of 
Aristotle,) not as in any way expressive of the passions or the 
will. Logic therefore solely regards words as the signs of an 
operation of the reason, and hence its simplest words are the 
noun and the verb, which alone are per se signs of conceptions. 
Syncategorems, being not significative but consignificative, 
are excluded from Logic, but recognised by Grammar. So 
Aristotle, in the De Interpretatione, treats only of the noun 
and the verb. In the Poetics, ch. 20. he adds the cf}a)va\ aaijixoi, 
the conjunction and the article. Cf. Harris, Hermes, ch. iii. 
On the distinction betw^een the logical and the grammatical 
proposition, some good remarks will be found in Du Marsais, 
Principes de Grammaire, p. 321. 

1 Supponit pro re. The supposition (as it was called) of a 
term being posterior to its signification. The doctrine of the 
supposition of terms, which is not found in Aristotle, is one 
of the subtleties of the parva logicalla, a scholastic addition to 
the Organon, rather grammatical than logical. Suppositio 
was defined to be " Acceptio termini substantivi pro aliquo ;" 



RUDIMENTA. 11 

lati, vocesque quas Natura sponte suggerit^ extra 
artem censentur. 

Jam, quae simplicem Apprehensionem exprimit. 
Vox Simplex e^t \ quae Judicium, Complexa" ; quae 
Discursum, Decomplexa. Nam argumentum omne 
resolvitur in tres Propositiones, sive sententias, et 
propositio omnis complectitur voces, non semper 
numero, sed sensu semper tres ; 1. Siihjectum, 

thus the term liomo, naturally applicable to men of all 
generations, is, in the proposition homo currit, accidentally 
limited to existing individuals. In this case it was said, in 
not very classical Latin, "homo supponit pro praesentibus." 
For further information on the various kinds of supposition, 
the curious reader may examine Sanderson's Logic, b. ii. 
ch. 2. 

' Vox complexa {(jicovT) o-v^Tveiikcyiievr)) in Aristotle signifies a 
compound word ; his example is cTraicTpoKeXrjs, of which each 
part has a meaning in composition. Vox simplex {diArj) where 
the parts have no meaning. The later meaning oivox complexa 
properly corresponds to Aristotle's X0709 (Oratio), and is not 
limited, as by Aldrich, to the Fropositlon (oratio enunciativa). 
Thus Petrus Hispanus : " Vocum significativarum ad placitum 
alia complexa, ut oratio, alia incomplexa, ut nomen et ver- 
bum. Orationum perfectarum alia indicativa, ut liomo currit; 
alia imperativa, ut Petre fac ignem ; alia optativa, ut utinam 
esset bonus clericus ; alia subjunctiva, ut si veneris ad me daho 
tibi eqiium ; alia deprecativa, ut miserere mei Deus. Harum 
autem orationum, sola indicativa oratio dicitur esse propo- 
sitio." Sum. Log. Tract. 1. Cf. Boeth. de Syll. Cat. p. 582. 
With regard to the vox decomplexa; as 'koyos is defined by 
Aristotle as a species of ^001/77, and syllogism as a species of 
\6yoi, the latter may without error be called vox. But the 
distinction is unnecessary; the syllogism, as far as apprehension 
is concerned, being only three several propositions. The con- 
nexion between them is not a matter of apprehension, but of 



12 ARTIS LOGIC/E 

sive de quo aliud dicitur. 2. Prcedicatum, sive id 
quod dicitur. 3. Copulam, quae utrisque media 
intercedit'. Nam Subjectum et Praedicatum quoad 
sensum semper extrema sunt, et vocantur ideo 
Termini Propositionis. 

Atque hinc adeo vulgo dicitur Pars prima 
Logicse versari circa Terminos simplices, i. e. voces 
simplices, Apprehensionem simplicem exprimentes* : 
secunda circa Propositionem, sive Vocem com- 
plexam, quae Judicium exprimit : tertia vero circa 
Syllogismum, sive Vocem decomplexam, qua Argu- 
mentatio sive Discursus exprimitur. 



^ The Latin Logicians distinguish between propositions 
secundi adjacentis, in which the copula and predicate form one, 
word, e. g. " Homo currit," and propositions tertii adjacentis, '] 
in which they are separated, e. g. " Homo est animaL" The * 
distinction originates with Aristotle, see De Int. 10. 3. But 
Aristotle does not maintain that propositions of the former 
kind are to be resolved into the latter. On the contrary, the 
early part of the De Interpretatione is adapted exclusively to 
propositions secundi adjacentis; and in order to make it ap- 
plicable to such propositions as " Homo est animal," we must 
consider the copula and predicate as equivalent to a single 
verb \ 

* In Aldrich's limitation of the terms. Vox simplex, Vox 
categorematica, and Terminus simplex, are synonymous : syn- 
categorems not being voces (logicse) at all. But in this 
usage he is not always consistent. 

* In De Int. 1. 4. it seems at first sight as if \evKhv alone was a prjixa. 
That this is not the case is clear from Poetics, 20. 9. rh (x\v yhp &vdpuiros 
^ \evKhu ov (TTjfiaii/ei rh ttSts, rh 5e fiaSi^ci ^ fie^dSiKe irpocrariiJ.aivei rh fxev 
rhv napSvTa xp^^ov rh Se rhu irap^XrjXvdSTa. In fact, \evK6y, by a common 
Greek Idiom, is equivalent to X^vkSv eVrt. 



RUDIMENT A. 13 

§. 3. Prima igitur pars Logicae versatur circa De int. eh. 
Terminos Simplices^ ; i. e. ejusmodi voces, quae 
solitariae in propositione praedicari vel subjici pos- 
sunt ; et vocantur ideo Categoremat'iccB, ut homo, 
lapis^. Quaedam etiam Vocabula sunt tantum 
Syncategoremata, sive compartes Subjecti aut Prag- 
dicati, ut omnis, nullus ; Quaedam etiaui mixta ^, ut 
semper, i. e. omni tempore ; nemo, i. e. nullus homo ; 
Currit, i. e. est currens ; quo etiam modo verbum 
omne Grammaticum resolvi potest. 

Verbum igitur Logicum (nempe purum) praeter 
Copulam nullum est : caetera ex participio et 
copula coalescunt". 

" Aristotle's Simjde terms, {opoi, eU ovs diaXverai fj irpoTaa-is,) 
or, as others call them, categorematic ivords, are the noun as 
subject, and the verb as predicate, " homo currit.'" The oblique 
cases of the noun and past or future tenses of the verb are 
not simple terms, being only nroiaeis ovofxaros or prjiiaros. The 
noun and verb are tlius the only two parts of speech re- 
cognised by Logic. See Boethius, In trod, ad Syll. p. 561. 
and Petr. Hisp. Tract. I. But it would be more accurate to 
say that Logic analyses language on a different principle, 
and hence does not recognise the grammatical parts of 
speech at all. The logical proposition should be of the form 
tertii adjacentis, and its predicate forms a part of the gram- 
matical verb. Cf. Prolegomena Logica, p. 274. 

" The terms categorematic and syncategorematic are not Aris- 
totelian, though the distinction is of course implied in his 
theory of the Proposition. YLarqyoprjyia in Aristotle means a 
predicable, e. g. de Int. 11. 4. Cf. Trendelenburg, Elementa, 
§. 3. Waitz, vol. i. p. 267. 

y Mixta. This is clearly a cross division. Every mixed 
word must, of course, be categorematic or syncategorematic. 

^ The copula has an apparent resemblance to the gram- 



14 ARTIS LOGICS 

Deint.2.1.' Nomen Logicum, est Terminus simplex sine 
/tempore significativus^ Nam ex antedictis. Ter- 
minus simplex idem valet atque Vox articulata et 
recta, et ex instituto significans : siquidem exclusse 
sunt voces inarticulatae, quasque natura sponte 
suggerit ; voces autem obliquae sunt Syncatego- 
remata. 

Multse sunt Nominis Divisiones ; quorum tres^ 
sufficiunt hujus loci instituto ; sed ob multiplicem 
earum usum, quinque alias adjungam. 

Deint.7.1. 1. Nomcn singular e, est quod rem unam et 
solam significat, ut Socrates: Commune, quod 
plura, et eorum singula significare potest, ut homo, 

matical verb, as being tbe only part of a logical proposition 
capable of personal inflection. But inflection is one of the 
accidents, not one of the essentials of a verb, and belongs 
to particular, not to universal grammar. The essence of a 
gi'ammatical verb lies in its signification, being a combination 
of an attribute and an assertion. Cf. Stoddart, Universal 
Grammar, p. 121. Latham, English Language, p. 461. The 
copula must of course not be confounded with the verb 
est, which predicates existence, as " Homo est." The whole 
question is ably treated by Pacius on de Int. ch. 3. Cf. Biese, 
PhilosopJiie des Aristoteles, vol. i. p. 95. 

^ Nomen. — Arist. de Int. 2. 1. ovofia jxev ovv earl (pcovr} aijfiavTiKTj 

Kara avvdfjKrjv avev xpovov. Sine tempore, as opposed to the verb, 
the other simple term, t6 irpocra-r^^xaivov xpovov. '■'Currit,'" e. g. 
in addition to its principal notion of running, signifies as an 
adjunct the present time, (see Ammonius, Scholia, p. 105. 
b. 29.) This distinction is lost when we resolve the verb 
into copula and predicate. 

^ Tres, i. e. the three employed in his definition of pra- 
dicabile, viz. those into singular and common, univocal and 
equivocal, first and second intention. 



RUDIMENTA. 15 

[2. Transcendens, quod solis omnibusque veris 
Entibus convenit, ut ens, res, aliqidd, uniim, verum, 
honum\ S iipertr ansae ndens, quod omnibus etiam 
fictis, ut imagmabile, cogitabile : Non-transcendens, 
omne aliud nomen.] 

3. Finitum, est cui abest particula non: Infi-Deims 
nitum^, cui praefigitur, ut non homo, i. e. omnia 
praeter hominem : unde particula non, dicitur in- 

Jinitans. 

4. Positivitm% est quod significat rem quasi prae- 
sentem : Privativum, quod dicit absentiam rei a 
subjecto capaci : Negativum, quod ab incapaci. ; 
Sic homo est vox positiva ; videns dicitur de homine 
positive ; cceciis de homine privative ; ccecus, seu 
potius non videns, de lapide negative, 

5. Univocum\ est cujus una significatio aeque Cat. i. : 

<^ These are usually called the six transcendents, and are 
regarded as predicable of the several categories analogously, 
not univocally. 

'^Infinitum. So translated by Boethius. It should be Mic?e- 1 
finitum; see Hamilton on Reid, p. 685. The translation is 
censured by Vives, de Caus. Corr. Art. lib. 3. 

*" In these divisions there is much clumsiness and self- 
repetition. The distinction between positive and privative 
nouns is repeated below, under the four opposita. Negative 
nouns have no business here at all, being opposed, not to 
positive, but to affirmative, and belonging to another kind of 
opposition, the contradictory. Belatives also form another 
member of the same fourfold division ; and Rcpugnants include 
all the four opposita, and other nouns to boot. 

^ Univocum {univocatum) — a-vvcawfxov: (Bquivocwn, {cequivo- 
catum) — ofMoovvfiov. 'O/xooi/u/xa Xeyerat 2)1/ ouo^a yiovov koivov, 6 8e 
Kara rovuojxa Xdyo? rrjs ova-ias erepos, olov ((oov o re avdpcoTTOs kol to 



/ 



16 ARTIS LOGICS 

convenit multis, ut homo : Mquivoctim, cujus 
^/ diversser ut Gallus : Analogum, cujus una inae- 
qualiter ut fes, [Vox ipsa dicitur Univocum Uni- 
vocaiis : res significata Univocum Univocatum, et sic 
de caeteris.] 

6. Absolutum^, est cujus tota significatio spectat 

yey pa^nxevov. '2vva>vvfJi,a de Aeyerai a>v to re ovoyia kolvov koL 6 Kara 
Tovi/ofxa Xoyos Ti]S ovaias 6 avros, oiov ^aov o re at/dpcoiros kolL 6 ^ovs. 
(Cat. ch. 1.) Analogous nouns are but one out of many 
species of equivocal, belonging to the cequivoca consilio, (diro 
biavoias,) of the Greek interpreters ; to which are opposed the 
cequivoca casu, (dno rvxns-) See Scholia, p. 42, a. 37, 47, 
Boethius in Prsedicamenta, lib. 1. p. 117. (Cf. Arist. Eth. Nic. 
i. 4. 12.) The o-wawfia of Aristotle must be distinguished 
from the modern synonyms, which answer to the 7vo\v6iWjjia of 
Speusippus, (Schol. p. 43. a. 31.) and the muUivoca of Boethius, 
and are defined by the latter, " quorum plura nomina, una 
definitio est." Swwi/u/xa was used in this sense by the Stoics, 
and the same sense may also be found in Aristotle, Ehet. iii. 
2. 7. and perhaps Top. viii. 13. 2. 

s It is not easy to distinguish accurately the two divisions 
of terms into absolute and connotative, abstract and con- 
crete, respectively. The following attempt is made with some 
doubt as to its success. In the second chapter of the 
Categories, Aristotle divides all ovra into four classes. Uni- 
versal Substances, Singular Substances, Universal Attributes, 
and Singular Attributes. Substances of both kinds exist i^er 
se; attributes can only exist in substances. Hence the 
scholastic distinction between Subjects of Predication and 
Subjects of Inhesion. The universal substances are pre- 
dicable of the singular, as genera and species of individuals. 
" Socrates is a man." In this case the individual is a subject 
of predication. Attributes are not in their original state 
predicable of substances. Whiteness exists in snow; but we 
cannot say, " Snow is whiteness." Here, then, the subject is 
not one of predication, but of inhesion. But, by an act of the 



RUDIMENTA. 17 

rem per se sump tarn, [ut Justitia : Connotativum, 
quod eandem quasi alteri nexam^ ut Justus,'] 
, Concretum, quod rem quasi sua natura liberam, sed 
jam implicitam subjecto, ut Justus: Abstractum, 
quod rem quasi sua natura nexam, sed jam subjecto 

mind, an attribute may be so connected with a subject as to 
become predicable of it as a differentia, property, or accident ; 
e. g. "snow is white." Predicates thus formed from attributes 
are called connotative, being said to signify primarily the attribute, 
and to connote or signify secondarily (Trpoa-arjfialveiv) the subject of 
inhesion. Hence a connotative term may be defined, " One 
which primarily signifies an attribute, secondarily a subject." 
Whereas the original universals, whether substances or at-^ 
tributes, as " man," or " whiteness," were called absolute. 
Again, by an act of the mind, the terms signifying substances, 
may be conceived in the form of attributes, so as to be no 
longer predicable of the individuals ; thus " homo " becomes 
"humanitas." All such terms, not predicable of singular 
substances, whether primarily attributes, as " whiteness," or 
secondarily conceived as attributes, as " humanity," are called 
abstract terms ; all that are predicable of the individuals, 
whether primarily, as "homo," or secondarily, as " white," are 
concrete. Hence the two divisions are distinct in principle, 
though some of the members of each cross. For example : 
Homo is concrete and absolute, albus concrete and conno- 
tative, albedo abstract and absolute ; but no abstract term is 
connotative. 

The above account differs considerably from that given by 
Mr. Mill, Logic, b. i. chap. 2. He inverts the phraseology, 
describing the attribute instead of the subject as connoted, 
and extends connotative terms, so as to include all concrete 
general names. This is in some respects an improvement on 
the scholastic distinction, but it must not be confounded with 
it. The materials of the present note are chiefly from Occam, 
Logic, p. i. chap. 5, 10. It must be admitted, however, that 
there is some licence in the use of the word connotative. 



18 ARTIS LOGICS 

Cat. 1. 5. exemptam, ut Justitia, [Denique, si Concretum 
sola termination e diversum sit ab Abstracto, ut 
Justus a justitia, hoc Denominans dicitur, illud 
Denominatwum, Subjectum vero Denominatum^, 
Cat. 8. 27. Denominalivis accensentur aliquando Derwativa 
ilia, quae vel solam nominis Analogiam, vel solam 
rei vim, non utramque retinent, ut Studiosus studii 
et virtutis, Sed ista verius Conjugata sunt\ 

Connotativum quoque dicitur de nominibus 
quorum conceptus se mutuo ingrediuntur, ut 
Poter et Filius : nam et ilia opponuntur absolutis ; 
sed vocantur proprio nomine Relativa.] 

7. Convenientia, sunt qu^ possunt de eodem 
simul dici, ut doctus et plus : Repug?iantia, sive 



^ Tlapavvixa Se Xe-yerai oaa aTrd tlvos biacfiepoirra rfj iTTaxrei ttjv Kara 
Tovvofxa Trpocrtjyopiav e-)(ei, olov aTro Trjs ypaixp.aTiKrjs 6 ypafip-ariKos Koi 
ano Trjs dvbpcias 6 avSpelos. Cat. i. 5. The word 7rapct)vvp.a is 
translated by Boethius denominativa. It should have been 
denoininata. From the same authority denominatives have 
been limited by the Schoolmen to concrete adjectives, pre- 
dicable of a subject possessing the abstract attribute. Cf. 
Aquinas, Opusc. xlviii. Tract. S. cap. 1. The limitation is not 
warranted by Aristotle, and is expressly rejected by his Greek 
Commentators. See Simplicius, Scholia, p. 43. b. 5. rSiv 8e 
7rapa>vvp,cov av e'ir), (prjalv 6 Ilop(f)vpLos, koi to. TrarpcovufxiKa Kal to. 

CrVyKpLTLKO. KoX TU VTTepOeTlKO. KOi TO. VirOKOpiCTTlKa.. 

i Studiosus is used in Scholastic Latin as a translation of 
the Greek airovdalos into the two senses of " diligent" and 
"virtuous." In the former, it is a denominative from studium. 
In the latter, not, as is observed by Aristotle, Cat. 8. 27. The 
name conjugata is more properly applied to derivatives from 
the same primitive, as sapiens, sapienter, sapientia; the ava-Toixa 
of Aristotle. Cf. Arist. Top. il 9, 1. Cic. Top. c. 3. _ 



RUDIMENTA. 19 

Opposita, quae non possunt, ut album et ni- 
grumK 

[Oppositio'' incomplexa, sive terminorum simpli- Cat. lo. i. 
cium, est omnino quadruplex : L Relativa, inter 
terminos relatives, ut Patrem et Filiiim, 2. Con- 
traria, inter contrarios, i. e. absolutes se mutuo 
pellentes ex subjecto alter utrius capaci, ut album 
et nigrum. 3. Privativa, inter privativum et posi- 
tivum, ut videntem et ccecum, 4. Contradictoria, 
inter positivum et negativum, intellige finitum et 
infinitum, ut hominem et non-hominem, Hasc est op- 
positionum maxima, quia nullum admittit medium ; 
neque Participationis, quale est fuscum respectu Cat. lo. 8. 
albi et nigri ; neque Abnegationis, quale est lapis 
inter videntem et coicum^, Relativa contra, omnium 

^ Repugnantia should not be considered as synonymous 
with opposita. There are many repugnants which are not 
included under any of Aristotle's four modes of opposition ; 
e. g. red and blue are repugnant, but not opposed. 

^ Aeyerai de erepov irepa avTiKela-daL rerpaxcdS, 77 o)S to. Trpos ri, fj 6)S 
TO, evavTia rj cos (rreprja-LS Ka\ e^is, /} o)s KaTd<paai9 KOi dnocfiaais. 
'AvriKeirai de eKcurruv tcov toiovtcov ois tvttco enreiv (os peu rd npus tl 
oXov TO dnrXdaiov rw fjpiicreiy cos 5e rd ivavria, olov to kukov rw dya3u>y 
0)? Se ra Kara (TTcprjcnv Koi e^iu, oloj> tvcJAottjs koL 6\lns, o)s Se KUTa- 
(jiaais KOL drrocpao-LS, olov KddrjTai ov Kd6r)Tai. Cat. 3 0. 1. Cf. Metaph. 

iv. 10. Contraries are the two most opposite qualities of the 
same class of subjects, e. g. black and white, as colours of bodies; 
virtue and vice, as habits of the soul. Cf. Cat. 11.5. 

* Medium Participationis. i. e. no object can be conceived 
as both A and not-A. This law of thought is called the Prin- 
ciple of Contradiction. Medium Abnegationis, i. e. no object 
can be conceived as neither A nor not-A. This law of 
thought is called the Principle of Excluded Middle. See 
above, p. 5. note j. 

c2 



? 



20 ARTIS LOGICiE 

minima; nam Relata non sunt opposita, nisi ad 
idem sumantur.] 

8. Nomen"" Primce intentionis, est Vox in com- 

™ " Oi the first intention,'" says Hobbes, " are the names of . 
things, a man, stone, &c. of the second are the names of names / 
and speeches, as universal, -particular, genus, species, syllogism,! 
and the like." Except that the language is too much adapted 
to the ultra nominalism of the author, this passage exactly ex- 
presses the true distinction. A first intention or notion is a con- 
ception under which the mind regards things, whether facts of 
external or of internal perception. Thus the individual Socrates 
is regarded by the mind as man, animal, body, substance. All these 
are first intentions. And a mental state may be successively 
regarded as a smell, a sensation, a fact of consciousness. These 
again ar-e first intentions. A second intention or notion is a 
conception under which the mind regards its first intentions 
as related to each other. Thus the relation of animal to man^ 
and of man to animal, is expressed in the second intention 
genus or species. First intentions, as conceptions of things, 
are predicable of the individuals conceived under them. 
Thus we may say, " Socrates is man, animal, &c." Second 
intentions are not so predicable : we cannot say, " Socrates 
is species, genus, &c." Hence when we are told that a 
predicable is commune, univocum, secundcB intentionis, it is not 
meant that all universals are in themselves second intentions ; 
but that every predicate viewed in relation to its subject may he 
comprehended under one of Porphyry's five classes af pre- 
dicables; all which are second intentions. So when Genus 
is said to be predicable of Species, it is not meant that we can 
predicate the one second intention of the other, so as to say, 
" Species is Genus ;" but that the first intention " animal" is 
predicable of the first intention " man ;" the relation of the 
one to the other being expressed by the second intentions 
" genus" and " species." For this reason Logic was said to 
treat oi second intentions applied to first. See Aquinas, Opusc. 
Ivi. Scotus, Sup. Univ. Qu. 3. Zarabella, De Natura Logicse, 
lib. i. cap. 19. ^ 



RUDIMENTA. 21 

muni usu posita. Secundce, Vox artis, quam ex 
communi sermone sumptam Philosophia recudit 
denuo et moderatur. 

§. 4. Vox Singularis, dicitur alio nomine Indi- 
mduum, ej usque significatum Unum numero : neque 
enim singulare est quicquid Unum dici potest; sed 
multa, quae sunt invicem similia, eatenus Unum 
censentur. Vocantur enim uno eodemque nomine ; 
quod ipsa Vocis definitio'' non patitur, nisi in illis 
reip^a sit, vel saltem concipi possit, una aliqua 
eademque Natura, quae huic nomini respondeat. 

Talem reperit intellectus, dum plura contem- 
plando ahstraliiV ab eorum differentiis; i. e. spectat 

The distinction between first and second intentions is 
generally considered as of Arabian origin. Scotus, however, 
(Sup. Univ. Qu. 3.) attributes it to Boethius, whose extant 
writings do not confirm the statement. It is found in 
Averroes, Epitome de Predicamentis ad fin. For scholastic 
expositions, see Aquinas, Opusc. xlviii. Tract. 1. cap. 1. in 
1 Sent. Dist. 2. Qu. 1. Art. 3. Scotus, in 1 Sent. Dist. 23. 
In Univ. Qu. 11. Occam, Logic, P. i. cap. ] 1. A good account 
of the formation of second intentions is given by Burgersdyck, 
Imt. Log. lib. i. cap. 2. Aldrich's definition, which is ex- 
tremely vague though not positively erroneous, was probably 
suggested by Crakanthorpe, who in his Prooemium calls 
second intentions Voces Artis LogiccB. It is scarcely necessary 
to add, that the explanation of Abp. Whately is altogether 
erroneous. 

° Vocis dejinitio. Since Vox is " signum rei vel conceptus,'" 
not rerum vel conceptuum. 

° Ahstrahit. i. e. abstracts its attention from the distinctive 
features of the objects presented. The terms abstract and 
abstraction have been used in various applications ; retaining 



22 ARTIS LOGIC.E 

in rebus ea tantum quae conveniunt, neglectis 
omnibus quibus dissident ; adeoque fundamentum 



however in all the primary signification of witlidrawing the 
attention from one portion of certain phenomena given in 
combination to fix it on the rest. In this sense Geometrical 
Magnitudes are called by Aristotle to. e^ dcfiaipecrecos, {An. Post. 
I. 18. 1.); because the Geometer considers only the properties 
of the figure, separating them from those of the material in 
which it is found. (See An. Post. I. 5. 6. Metaph. x. 3. 7.) 
On similar grounds is formed the scholastic distinction of 
abstract and concrete terms ; since in the former the attribute 
is considered apart from the subject in which it is perceived 
by the senses : e. g. sight presents to us only alba; the mind 
forms the conception albedo. And so Universals are gained 
by abstraction, i. e. by separating the phenomena in which a 
given group of individuals resemble each other from those in 
which they differ. For this reason Locke calls all universals 
abstract ideas ; a phrase etymologically allowable, but liable to 
be confounded with the scholastic use of the word abstract in 
a different sense. For this reason it is better to adhere to the 
term universals ; which has at the same time the advantage of 
leaving the Logician, as such, uncommitted to any metaphysical 
hypothesis as to their nature ; since the Realist may interpret 
Universal Substances, the Nominalist, Universal Names, the 
Couceptualist, Universal Notions. 

Generalization, which some modern writers distinguish from 
Abstraction, is pi'operly a species of abstraction ; viz. the divest- 
ing the presentations of consciousness of the conditions of 
existence in space and time, which are characteristic of indi- 
viduals. This is done by the aid of signs, verbal or other, 
which are at first signs of individual objects, and subsequently 
of general notions. Other abstractions may exist without gene- 
ralization ; but these are not processes of thought, but of per- 
ception, internal or external. Thus, to fix the eye or ear on 
a particular sight or sound exclusively, is in the widest sense 
an abstraction, but not a generalization. The psychological 



RUDIMENTA. 23 

omne discriminis, praeter numerum, eximit. Quare 
naturam sic abstractam, cum sit omni singulorum 
differentiae superstes, concipi par est, non ut in 
singulis diversam, sed ut in omnibus eandem ; 
adeoque Universale quiddam sive Ens unum in '. 
muUisj ej usque signum idoneum eril,' Nomen j 
commune, Univocum, Secundce intentioms,m\o verbo, / 
Prcedicabile^ , sive Vox apta praedicari, i. e. Univoce 
dici de multis. 

§. 5. Pr^dicabilium"^ capita, constitui et 

controversies concerning abstraction cannot be discussed 
here. See Prolegomena Logica, p. 25. 

p " Prsedicabile (Grasce KaTrjyopovfxevov) et universale, etsi 
reipsa non differant, (omne enim universale prsedicari potest, 
et omne prsedicabile debet esse universale,) ratione tamen 
diversa sunt. Nam universale, quatenus universale est, prsB- 
dicatur de inferioribus, in qupestione qua quseritur quid sint : 
at prsedicabile, quatenus est prasdicabile, prasdicatur etiam de 
coordinatis, idque in qusestione qua qureritur qualia sint. 
Itaque, cum quinque sint prsedicabilia, tantum duo tamen 
universalia sunt, genus et species. Nam differentia, proprium, 
et accidens, quatenus talia sunt, non sunt universalia, sed 
tantum quatenus sunt genera aut species eorum qu^e sub illis 
continentur. Ex. gr. Sensus est proprium animalis ; sed non 
est universale, quatenus ut proprium de animali praedicatur, 
sed quatenus praedicatur de visu, auditu et cseteris sensibus, 
ut genus." Burgersdicii Inst. Log. 1. i. c. x. The addition of 
uyiivocum, secundce intentionis is supei'fluous. The latter has 
been explained in a former note. The former, though a 
necessary result of the abstraction here described, is not 
a necessai7 part of the notion of a predicable. Indeed, other 
Logicians distinguish between (Equivocal, univocal, and denomi-j 
native predication. See Sanderson, 1. i. c. 6. 

"^ The five Heads of Predicables are an addition to the 



24 ARTIS LOGIC.E 

definiri possunt ad hunc modum. Quicquid in 
multis reperiri potest, vel est tota eorum essentia, 
vel ejus pars, vel cum essentia conjunctum '. 
Quare Universalia vel (quod eodem redit) Prae- 
dicabilia sunt quinque, et non plura ; videlicet. 
Genus, Species, Differentia, Proprium, Accidens, 



Aristotelian Logic, taken from the Isagoge or Introduction 
to the Categories by Porphyry, written in the third century. 
Aristotle's doctrine, as far as it can be gathered from the 
Topics, differs from that of Porphyry in several points; as 
does the latter from the view adopted by Aldrich. 

^ Quicquid in multis, &c. These definitions are taken from 
Albertus Magnus, (de Praedicab. Tract. 11. cap. 1.) and were 
generally adopted by the Kealists, in the form of introduction 
to, or commentary on, the Definitions given by Porphyry. 
The Nominalists, on the other hand, expressly denied that 
any predicable was of the essence of the individual. See 
Occam, Logica, p. i. cap. 20, 21. To discuss the full bear- 
ings of this controversy would exceed the limits of a note. 
It will be sufficient to observe, that a considerable portion of 
the language adopted by Aldrich is not even intelligible, 
except on reaUstic principles ; and that whenever the same 
language is adopted by a Nominalist, he is inevitably involved 
in inconsistencies and self-contradictions. The same is in 
some degree true of the original exposition of Porphyry, 
though the latter professes to leave the question of Nomi- 
nalism and Realism open. But the question of the existence 
of universals a j^cifte rei is metaphysical, not logical, and 
no theory on this point ought to influence the language of 
Logic. The rules of Logic are primarily regulative of 
thoughts; and equally so, whatever opinion we may hold 
concerning the essence of things. For this reason, it is 
necessary to alter nearly the whole of Aldrich 's language, 
in speaking of the logical predicables. On the realist point 
of view, see further. Appendix, note k. 



RUDIMENTA. 25 

Nam ] . Genus y est quod prasdicatur de pluribus Porph. 
ut eorum essentiae pars materialis sive communis ; 
ut animal^. 2. Differentia, quae ut essentiae pars 
formalis sive discretiva ; ut rationale. 3. _ Species , ^^^s-^- ^- 

' -f"— '17,20. 

quae ut tota essentia ; ut homo. 4. Proprium, 
quod ut essentiae junctum necessario ; ut risibile. 
b. Accidens, quod ut essentiae junctum contin- 
genter ; ut album, nigrum, sedere\ 

^ " Genus speciebus materia est. Nam sicut ?es, accepta 
forma, transit in statuam, ita genus, accepta differentia, transit 
in speciem." Boethius de dtvisione. But as logicians, we are 
not warranted in introducing any portion of the essence of 
things, but only of concepts or general notions. The whole 
essence of a concept is the sum of the attributes which it 
comprehends, and this can only be fully declared by its 
dejinition, not, as Aldrich says, by species. The Genus or 
material part of two given concepts, (to speak of the material or 
formal part of a single concept is nonsense,) is the sum of 
those attributes which are common to both ; as the difference 
or formal part is composed of those attributes which are 
peculiar to each. Thus, if there be given three concepts, 
containing respectively the attributes, ah, ac, he, a is the 
genus of the first compared with the second, h and c the 
respective differences. But if the first is compared with the 
third, h becomes the common genus, a and c the respective 
differences. In this, the only tenable logical point of view, 
there can be no such thing as an absolute genus or 
difference. 

^-Necessario — Contingenter. This distinction is based on 
the supposition that certain attributes are necessarily con- 
nected with others, from which they flow, as effect from 
cause. Thus risibility was described in the scholastic philo- 
sophy as necessarily flowing from rationality, in the same 
manner as having the angles at the base equal to each other 
necessarily results from the equality of two sides in an 



26 ARTIS LOGICiE 

Patet hinc P. De iis did Prcedicabile quibus 
inest Universale. Genusque adeo, quod est plu- 

isag.2. 11. rium essentiarum vel specierum pars communis, 
de specie differentihus, h. e. de diversis speciebus 
quas ingreditur, dici ; ut animal de homine et hruto. 
Speciem vero, de numero differentihus, h. e. de 
diversis individuis, quorum singula habent essen- 
tiam speciei vocabulo significatam ; sic homo de 
Socrate et Plaione dicitur, et de omnibus^ quibus 
natura inest humana. Reliqua vero Prasdicabilia, 
(prout inferius patebit) eadem de causa, tam de 
specie quam numero difFerentibus dicuntur. 

Et N. B. ex recepto more loquendi. Genus et 
Speciem prcedicari in (i. e. respondere qusestioni 

Top. iv. 2. factae per) Quid"" ; DifFerentiam in Qualequid; 

Isag.2. 13. 

10.5.11.5. isosceles triangle. But this theory, originally borrowed from 

' * the mathematics, is not true of any succession of physical 

phenomena. As a matter of fact, we experience that certain 
events are invariably conjoined, but there is not, as in mathe- 
matical demonstrations, any necessity that they must be so. 
Invariable succession, in fact, is the highest positive notion 
of causality to Avhich we can attain in the case of sensible 
phenomena, though this limitation does not include the 
moral causality of which we are conscious in volition. Neces- 
sity, however, in any sense is untenable as a logical criterion 
of property, since it presupposes an acquaintance with the 
laws of any given physical phenomena, of which the Logician 
as such knows nothing. A better logical distinction between 
property and accident is that given by Aristotle, of the con- 
vertible and 7ion convertible attribute. See Apj)endix, note A. 

•^ Pr(sdicatur in Quid ; i. e. is expressed by a noun substan- 
tive : in Quale; by an adjective. See Aquinas, Opusc. xlviii. 
cap. 2. (Of. Abelard, De Oen. et Sp. p. 528. ed. Cousin.) That 



RUDIMENTA. 27 

Proprium et Accidens in Quale, Unde facile est 
conficere vulgatas Praedicabilium definitiones. 
Nam Genus definitur, Prcedicahile quod prcedicatur 
de pluribus specie differ entibus in Quid, Differentia, isag. 2. 8. 
quod de pluribus specie vel numero differentlhus in 
Quale quid &c. "" isag. 3.17. 

Patet 2". Genus esse Totum quiddam. nempe Arist. 

,. Metaph. 

Logicum, sive in modo loquendi; quatenus con- iv.25.8,3. 
tmet (1. e. prsedicationis ambitu complectitur) 
species tanquam partes sui subjectivas, Speciem 

the distinctions of substance, quality, and the other categories, 
are founded on grammatical grounds, is shewn by Trendelen- 
burg, Excerpta, §.3. 

The reader of Locke must not confound this distinction 
with that between substances and modes; Essay, b. ii. ch. 12. 
(Cf. Descartes, Princ. i. 48. Port-Eoyal Logic, p. 1. ch. 2.) 
A quality is predicated in quid of another quality, as well as 
a substance of a substance ; e. g. " Prudence is a virtue." Cf. 
Pacius on Top. i. §. 3. Port-Royal Logic, part i. ch. 7. 

The distinction between Qualequid and Quale is not 
warranted by Porphyry. According to him, Differentia, Pro- 
prium, and Accidens are all predicated, eV rco ottoIov tI i<mv. 
Boethius distinguishes them as Quale in substantia and Quale 
non in substantia. The vulgatcB definitiones which follow are 
the original definitions of Porphyry, adopted by most subse- 
quent Logicians. 

'' Sj^ecie vel numero, i. e. generic difference de specie dif- 
ferentibus ; specific, de numero differentibus. But this would not 
be allowed by Porphyry, according to whom differentia is 
always predicated de specie differentibus. The remaining 
definitions might be supplied as follows; Species, quod de 
pluribus 7iumero differentibus in Quid. Proprium, quod de 
pluribus numero differentibus in Quale. Accidens, quod de plu- 
ribus genere vel specie vel numero differentibus in Quale. The 
two last, however, are not given as definitions by Porphyry. 



28 ARTIS LOGICiE 

quo que Totum esse, nempe Metaphysicum, sive in 

modo concipiendi ; quatenus continet (i. e. ad per- 

fectionem sui postulat) Genus tanquam partem sui 

isag. 3. 7, essentialem^ . Unde Differentia Generi accedens, 

13 

dicitur Genus ipsum dividere, quatenus ejus signi- 
ficata distinguit, et speciem constituere, quatenus 
ejus essentiam complet. 
isag. 2.23, S. 6. Genus aliud Summum, aliud Subalter- 

28. 

num est : Species quoque, in Subalternam et 
isag.2.23, /;z^ma?72 distinguitur^ Genus summum, est quod 

tia, 

y Totum Logicum — Totum Metaphysicum. The propriety of 
this nomenclature may be questioned. " Universale," says 
Burgersdyck, " totum quoddam est; quippe multa complectitur 
ut partes. Dicitur totum Logicum, quia Logicae munus est de 
universis disputare. Genus et differentia distinguuntur sola 
ratione ; ideoque compositio ex genera et differentia non est 
vera compositio, sed compositio rationis. Hoc totum solet 
appellari totum Metaphysicum, quia Metaphysica versatur circa 
ea fere, quae non tam reipsa quam ratione diversa sunt." 
Inst. Log. 1. i. c. 14. But in truth, as regards mere notions, 
the potential extension and comprehension are both within 
the province of Logic ; and as regards things, the real essence 
of a species and the actual subdivisions of a genus are both 
equally without. The distinction itself is of great importance, 
and has been expressed in various ways, by the terms potential 
and actual whole, whole in predication and in definition, uni- 
versal and essential whole, &c. The best is that adopted by 
the Port-Eoyal Logicians, who distinguish the extension or 
subjects of which a notion is predicable from the comprehen- 
sion or attributes which it involves in itself. Thus genus is 
a whole in extension, species a whole in comprehension. On 
this important distinction, see the Introduction to Mr. 
Baynes's Translation of the Port-Royal Logic, p. xxxii. or 
Mr. Thomson's Outline of the Laws of Thought, p. 128. 
^ The Summum Genus and the Infima Species, as here 



RUDIMENTA. 29 

nulli% Species infima, quae omni cognato Generi 

described, are both merely imaginary limits, never arrived at ■ 
in any process of actual thought. The notion of Being or | 
even of Substance in general, apart from this or that special ; 
combination of attributes, and that of a combination so 
complex as to admit of no additional attributes in thought, 
are both psychologically inconceivable. A Highest Genus 
and a Lowest Species may be admitted in any material 
science, as the limits at which the investigations of that 
science begin and end ; but such a limitation is made entirely 
on material grounds, relatively to the purpose of that par- 
ticular science, and cannot be recognised by Logic. Seei 
Appendix, note A. 

* The Aristotelian Logicians consider the summa genera as 
ten in number, viz. the ten Categories or Predicaments of 
Aristotle. These are ova-la, tvoctov, ttolop, npos n, ttoO, rrore, KeiaOai., 
exeiv, TToteTi/, irda-xeiv ; usually translated, Substance, Quantity, 
Quality, Relation, Place, Time, Situation, Possession, Action, 
Passion. The Categories have by different commentators 
been regarded as a classification of names, of things, and of 
both; and have been alternately banished to Metaphysics 
and recalled to Logic. Whatever position they may hold in 
the Metaphysical writings of Aristotle, in his Logical ones 
they are expressly declared to be a division of the notions 
signified by simple terms. Ens (t6 6v) was not regarded as a 
summum genus to the several Categories, being considered by 
Aristotle and his followers as predicable of them, not uni- 
vocally, but equivocally, or rather analogously. But a classifi- 
cation of Categories is out of place in Formal Logic. From 
the analysis of any notion, whether given in itself or as form- 
ing' part of a judgment, I can by mere thinking arrive at the 
simplest elements it contains ; but I cannot by mere think- 
ing determine that all notions so analysed will lead me to 
exactly ten such elements, neither more nor less. This 
requires a knowledge, not merely of all the forms of thought, 
but also of all the characteristics of the objects about which 
we can think. On the principle of the Aristotelian Cate- 



30 ARTIS LOGICiE 

isag.2.24, subjicitur : Genus vel Species subalterna^ quae et 

30 

cognato Generi subjicitur, et de cognata Specie 
praedicatur. Voco autem Cognata, quae ex iisdem 
Individuis perpetua abstractione colliguntur ; ut 
Homo, Animal, Vivens, Corpus, Substantia: quae 
ex Socrate, Platone &c. expurgatis continue difFe- 
rentiis oriuntur. 

[Hanc seriem ita placuit describi ut quodam- 
modo referret arborem : saltern a Porphyrio sic 
descripta Porphyriance Arboris'' nomen habet. 
Hujus truncum referebat linea direct a, in qua 
Genera et Species scribebantur : in suprema Tabula 
Genus summum^ in ima Species infima ; unde 
Nomina. Inter haec Media Subalterna, suo 
ordine. 

Differentiae ad latus sunt dispositae ; ad quas 
ductae a Generibus suis lineae Ramorum instar 
pertinebant. Individua sub specie infima oblique 
descripta sunt, quasi propagines Radicis.] 



gories and the objections raised against them, see Appendix, 
note B. 

^ Species suhalterna. Here the word species has changed 
its meaning. In the original definition it meant a certain 
relation in which a predicate may stand to its subject. Man 
is a Species to bocrates. It now nieans a certain relation in 
which a subject may stand to its predicate. Man is a Species 
to Animal. These are generally distinguished by Logicians 
as the species prcedicabilis and the species suhjicihilis. 

c By the Greek Logicians it was sometimes called the 
ladder {Kklyia^) of Porphyry. 



RUDIMENTA. 



31 



Arbor Porphyriana^ 




Socrates 



Plato 



^ This delineation of the Arbor Porphyriana is first given 
by Aquinas, Opusc. xlviii. Tract, ii. cap. 3. In all the earlier 
specimens, Animal Eationale is placed between Animal and 
Homo as the proximum genus, and divided into mortale and 
immortale, in accordance with Porphyry's definition of Man. 



32 ARTIS LOGICiE 

isag. 3. (3, Quare 1. Differentia est vel Generica, quae 
constituit Speciem Subalternam ; vel Specifica^, 
quae infimam : haec est, quae de numero diiFeren- 
tibus, ilia, quae de specie difFerentibus praedicatur. 
Exempla, Sensibile et Rationale, 

2. Proprium^ quoque, vel Geneiicum est, quod 
necessario comitatur essentiam Generis summi vel 
subaltern!^ ; atque ex ilia adeo fluere atque oriri 

^ The term specific difference (^dia(f)opa eldonoLoi) has a different 
meaning in Porphyry. It is opposed to accidental difference, 
{8La(})opa Kara (TVjx^e^r^Kos,) and marks the differentia proper, 
which distinguishes species from species, (whether subaltern 
or infima,) as opposed to accidents, which only distinguish 
between individuals. 

^ Proprium. In formal logic, which cannot take into 
account the realist theory of essence, it becomes necessary 
to change slightly the language which expresses the dis- 
tinction heUve en proprium and differentia. The essence of a 
concept is the sum of the attributes which it comprehends. 
Whatever does not form a part of the comprehension of the 
concept or of the signification of its name, is not part ofi but 
joined to the essence : i. e. it is found in all or some of the 
individuals of the class, but is not implied in the name or 
notion of the class itself. Thus it is no part of the notion of 
a triangle that its angles are equal to two right angles ; and it 
is no part of the notion of a body to have weight. These then 
are properties, not differences, and, when predicated of their 
respective subjects, form what Kant calls synthetical, as dis- 
tinguished from analytical judgments. Thus the non-essential 
are distinguished from the essential predicables. The further 
distinction of property from accident, as necessarily or con- 
tingently ]Ouiedi, has been already noticed as extralogical. 

s A summum genus can manifestly have no constitutive 
differentia; but it may have properties. There may be attri- 
butes forming no portion of the universal nature (or concep- 
tion) of substance, which are notwithstanding found in all 



RUDIMENTA. 33 

dicitur : vel Specificum, quod fluit ab essentia 
speciei infimae: lllud itaque de pluribus speciebus, 
hoc, de una specie et pluribus Individuis prasdi- 
catur. Exempla, Mobile et Rislbile. 

Proprium tamen aliunde quadrifariam dicitur \ isag. 4. i. 
1. Quod convenit soli, sed non omni; scil. soli 
Speciei, sed non omni ejus Individuo ; ut homini 

substances and at all times. Such properties of the summum 
genus are enumerated by Aristotle, Categ. ch. 5. These 
were in the scholastic theory regarded as flowing from the 
simple essence ; those of all subordinate classes from the 
differentia. 

^ Porphyry, following Aristotle, does not distinguish Pro- 
perty from Accident as flowing necessarily from the essence, 
but as coextensive and simply convertible with its subject. 
In this he is followed by Boethius; the other distinction, how- 
ever, appears as early as in the commentary of Albertus Magnus, 
and seems to have been derived from the Arabians. (Cf. Albert 
de Predicab. Tract, vi. cap. 1.) The 'l8iov of Porphyry answers 
to the fourth kind of property mentioned in the text. The 
other three are accidents; the first and third separable; the 
second inseparable, but still only an accident, as being pre- 
dicable of more subjects than Jiomo. On the scholastic theory, 
it is also an accident, as not flowing necessarily from rationale, 
the difi'erentia. Aristotle, who defines man C<pov ne^ov diTrow, 
would regard bijjes as a differentia. It may be observed that, 
upon the principles of Aristotle and Porphyry, a generic 
property can only be regarded as a property with respect to 
the highest species of which it is predicable. As regards all 
subordinate species, it must be considered as an accident.^ 
Mobile-, for example, a property of corpus, is an accident to 
animal, and to Jiomo, as not convertible with them. This may 
be fairly inferred from Top. ii. 3, 5. and is also maintained by 
Avicenna and Albertus Magnus : see Albert, de Predicab. 
Tract, ix. cap. 1. On the theory of necessary connexion, it may 
remain a property ; but on this authorities are divided. 

D 



34 ARTIS LOGICiE 

esse Grammaticum. 2. Qaod omni, sed non soli ; 
ut homini esse hipedem. 3. Quod omni et soli, sed 
non semper ; ut homini canescere. 4. Quod omni, 

isag. 14. 7. soli, et semper; ut homini risibilitas. Hujusmodi 
Proprium est, quod constituit Quartum Praedi- 
cabile. 

Isag. 5. 1. Accidens, cum essentise junctum sit contin- 
genter, adesse igitur vel abesse potest, salva interim 
essentia subjecti; cui tamen aliquando tam tena- 
citer inhagret, ut cogitatione sola divelli atque 
separari possit ; ut Mantuanum esse, a Virgilio. 
Quare vocatur Inseparabile\ Quod autem actu 
sive reipsa separari potest, ut albedo a pariete, 
dicitur Separabile, 



An. Pr. I. §. 7. QuEMADMODUM Vox Singularis dicitur Indi- 

31.1. 

An. Post. 

II. 6. 1. ' We must distinguish between the accidents of a class and 

II. 13. 7. ^i-jose Qf an individual. Of the former, those are inseparable, 

which, though not connected with the essence by any law of 

causation, are as a matter of fact found in all the members of 

the class, and can be the predicates of an universal proposition; 

e. g. " all crows are black." The separable accidents are found 

in some members of the class and not in others, and therefore 

can only be predicates oi particular propositions ; e. g. " some 

horses are black." This distinction between the separable 

and inseparable accidents of a class has been transferred by 

Archbishop Whately to distinguish between accident and 

property. Of the accidents of the individual, the inseparable 

can be predicated of their subject at all times ; e. g. " Virgil 

is a Mantuan ;" the separable only at certain times ; e. g. 

"Virgil is sitting down." Aldrich's distinction, between 

separable in thought and separable in fact, is extralogieal. Logic 

is concerned only with thought, not with physical changes. 



RUDIMENTA. 35 

viduum, ita et Communis Dividua dici potest. 
Earn enim per Metaphoram dividere dicitur^ qui 
plura ejus significata recenset; nam in uno raulta 
distinguit. Ita qui animal dicit esse (i. e. voca- 
bulum animal significare) hominem et hrutum, 
dicitur animal In hominem hriitumque dividere, 
Quare Divisio^, est distincta enumeratio plurium, 

^ Division was employed by Plato and others as a method 
of demonstrating definitions. Aristotle shews that the rea- 
soning is unsound, and always involves a. petitio princijni. For 
this reason he calls it a kind of weak sylTogism, tHough he 
allows it to be useful for testing definitions when gained : see 
Appendix, note C. Among the later Peripatetics, Division 
seems to have been held in higher estimation ; a separate 
treatise on the subject having been composed by Andronicus 
Rhodius. From them it descended to Boethius, whose book 
de Divisione is the principal authority from which subsequent 
Logicians have drawn. 

According to Boethius, the word Division is used in three prin- 
cipal senses. 1. Division of a genus into species. 2. Division 
of a whole into parts. 3. Division of an equivocal term into 
its several significations. Of these, according to Cicero, Top. 
eh. 6. the first is properly called Divisio, the second, Partitio. 
'' In partitione quasi membra sunt; ut corporis, caput, humeri, 
manus, latera, crura, pedes, et cetera: in divisione, formse sunt, 
quas Grseci ideas vocant; nostri, si quihcEC forte tractant, species 
appellant." Cf. Quintil. v. 10. vii. 1. In Division, the whole 
or ita definition can be predicated of each part, as " Homo est 
animal," " Homo est vivens sensibile." In Partition this can- 
not be done. Boethius, however, includes under his second 
head, not only the enumeration of the component parts of an 
individual, but also that of the individuals contained under an 
injima species. " Ut cum dico domus aliud esse tectum, aliud 
paries, aliudj fundamentum ; cumque hominis dicimus partes 
esse Catonem, Virgilium, Ciceronem." The last in one respect 

d2 



36 ARTIS LOGICiE 

quae communi nomine significantur. Estque ana- 
loga distribution! totius in partes. Unde et nomen 
ipsum Commune dicitur Totum Divisum, et dis- 
tincta ejus significata. Partes sive membra divi- 
dentia, et bene dividend! leges statuuntur tres. 
1. ^ Dividentia sigillatim minus contineant (i. e. 

more resembles division proper; as the name and definition of 
the whole are predicable of each part. But on account of the 
infinite number of individuals, and consequent impossibility 
of exhausting the species, this is not generally reckoned as a 
division proper. 

The division of an equivocal term, as canis into animal, 
sidiis, piscis, is sometimes called Distinction. The test of this 
is, that the name is predicable of each member, but not the 
same defi.nition. This is useful for separating the sense of 
an ambiguous term before defining it. See Top. vi. 2. 1. 

1 For the due observance of these rules, it is desirable that 
the division consist of as few members as possible. Some 
recommend dichotomy, or a division of every genus into two 
species by means of opposed differentiae. Of the foui' kinds 
of Opposition, Boethius admits for this purpose contraries, 
positive and privative terms, and also contradictories as some- 
times unavoidable; but rejects relatives. Aristotle censures 
the use of privative and indefinite terms, and approves of 
division by contraries. See (Top. vi. 6. 3. de Part. Anim. i. 3.) 
Here dichotomy is only practicable when the contraries admit 
no medium between them. Cf Cat. 10, 18. Top. vi. 6. 1. 
Examples of dichotomy by contraries may be found in the 
Arbor Porphyriana. For a threefold division of the same kind, 

see Eth. Nic. vii. 6, 5. Ta>v yap rjbecov evia (jivaei alperd, to. d' ivavria 

TovTcov, TO. be fiera^v. Dichotomy by contradiction, which Aristotle 
censures, had been a favourite method with Plato, as it after- 
wards was with Ramus and his followers. See Hamilton's 
Reid, p. 689. Cf Trend. Elem. §. 68. Erlauterungen, p. 106. 
But none of the above methods of division can be regarded 
as a strictly formal process of thought. Any concept A is 



RUDIMENTA. 37 

arctius significent) quam Divisum. Nam Totum a:op. vi. 
est majus partibus singulis. 2. Dividentia con- ' 
junctim plus minusve ne contineant quam Divisum. 
Nam Totum est aequale partibus universis. 3. Mem- 
bra Divisionis sint opposita, (i. e. in se invicem ne 
contineantur :) nam sine distinctione frustra est 
partitio. 

§. 8. DivisiONEM excipit"" (quae per Metapho- 

potentially divisible into A which is B, and A which is not B; 
and experience alone can determine whether either of these 
members includes under it really existing individuals or not. 
Logically, the division of animal into mortal and immortal is 
as good as that into rational and irrational. But this division 
is not strictly formal ; for B, the dividing attribute, not being 
part of the comprehension of A, has to be sought for out of 
the mere act of thought, after A has been given. This has 
been observed by Hoffbauer and Fries, who hence rightly 
maintain, against Kant, that even dichotomy by contradiction . 
is not an act of formal thinking. Cf. Hoffbauer, Logik, §. 138. 
Fries System der Logik, §. 92. 

The only strictly formal process of this kind is that 
distinguished as Determination, which consists in the reunion of 
a genus and difference previously elicited by analysis from 
a given concept. Formal Division thus presupposes Defi- 
nition. See Drobisch, Neue Darstellung der Logik, §. 17, 29, 30. 

" Excipit. The reason of this order is given by x\belard : 
" Quoniam vero divisiones definitionibus naturaliter priores 
sunt, quippe ex ipsis constitutionis suse originem ducunt, in 
ipso quoque tractatu divisiones merito priorem locum obtine- 
bunt, definitiones vero posteriorem." Dialectica, ed. Cousin. 
p. 450. This is true in a material point of view ; the matter 
of a definition being sometimes gained by division. But 
formally, the reverse order is preferable ; a formal division 
or determination being only possible after definition. See 
the last note. 



38 ARTIS LOGICS 

ram quoque dicitur) Definiiio ; cujus est, assignare 
conceptus et voces, quibus ea, quae ab invicem 
distincta volumus, velut agrorum fines, ex limitibus 
suis dignoscantur. Quas cum definitis notiora esse 
debeant magisque obvia, Definitio vulgo dicitur 

Top.i.5.L Oratio explicativa definiti. Oratio (inquam) ut a 
nomine distinguatur ; Explicativa quoque, nam et 
nomen exprimit. 

An. Post. Definitio alia, Nominalis est, quae vocis signifi- 

II. 7. 5. . . 

cationem aperit ; alia, Realis, quae rei"" naturam. 

° Rei, i. e. of an universal notion existing in the mind ; with- 
out entering on the question whether there exists any external 
universal nature corresponding to it. Since all such notions 
are represented by words, a real, or more correctly speaking 
a notional, definition, will at the same time unfold the meaning 
of 'tEe^vord by wliich the given notion is represented. Still ; 
the two kinds of definition must not be confounded. A real ■ 
definition has primarily for its object to analyse a complex j 
notion into its component parts. Words are employed \ 
secondarily, though unavoidably, as signs, both of the whole ; 
notion, and of the simpler notions of which it is composed, j 
sBut the object of nominal definition is to determine of what! 
hotion, simple or complex, a given word is the sign. The I 
notion may be abeady known, more or less clearly, by means 
of other signs, though we were not aware of its connexion 
with the word in question. A different distinction between 
nominal and real definition is given by Leibnitz, Nouveaux 
Essais, 1. iii. c. 3. 

If this account of real definition is correct, it will follow 
that the same notion admits of only one definition; since 
the same notion cannot be a combination of more than one 
group of attributes. And nothing can be more clear than 
Aristotle's testimony on these points, nothing more positive 
than his repudiation of the so-called accidental and physical 
definitions. (Cf. Top. vi. 4, 2. vi. 14, 5. i. 8. 2, 3. Metaph. vi. 



RUDIMENTA. 39 

Realis iterum vel Accidentalis, sive Descriptio, quae 

definite accidentia (puta causas, efFectus^ propri- 

etates aliaque id genus) assign at ; vel Essentialis, 

quae partes essentiae constitutivas. Essentialis 

denique, vel Metaphysica sive Logica'', quae Genus 

11, 15.) Nevertheless, on the strength of a misunderstood 
passage in the De Anima, (i. 1, 16.) the threefold division of 
real definition has been fathered on the Stagirite. For a 
fuller account of Aristotle's doctrine, see Appendix, note C. 
Before quitting this subject, it may be observed, that Logicians 
have perpetually confounded the thing or notion within the 
mind with the things or individuals without, i Thus Abp. 
Whately observes, that Logic is concerned with nominal 
definitions only ; because all that is requisite for the purposes 
of reasoning is, that a word shall not be used in different 
senses ; a real definition of any thing belongs to the science 
or system which is employed about that thing. On the 
contrary, Logic is concerned with real or notional definitions 
only: its object being to produce distinctness in concepts, which 
are the things of Logic. Nominal definitions belong to the 
grammars or dictionaries of particular languages. Even 
Kant (Logik, §. 106.) has not quite avoided this confusion. 

° Metaphysica sive Logica. On this point the two great sects 
of the Schoolmen were at issue. The Realists, following the 
Arabians, divided Logic into two parts ; one, which treated 
of the essence of incomplex notions and things by definition; 
the other, of the truth of propositions as determined by 
argumentation. To this latter the greater part of the Aristo- 
telian Logic was regarded as belonging. The former was 
supposed to have formed a lost portion of the ancient science. 
The Nominalists, on the other hand, and more correctly, main- 
tained that to investigate the essences of things belonged to 
the province of Metaphysics ; the Logician, as such, assigning 
no actual definitions, but borrowing them as mere examples 
from the science to which they properly belong. As autho- 
rities for the two views, compare Albert, de Prsedicab. Tract, i. 
chap. 5, 6. with Occam, Logic, part i. chap. 26. 



40 ARTIS LOGICiE 

et DifFerentiam ; vel Physical, quae partes Essentiae 
physicas, i. e. realiter distinctas : nam Genus et 
Differentia sola mente distinguuntur. 

E. g. Definitur homo Nominaliter'^, qui ex humo. 

p Physical definition is rejected by Aristotle, (Metaph. vi. 
11.) on the ground that the physical parts are not parts of the 
species, but of the individuals. Aldrich's expression, " partes 
essenticB physicas," cannot be tolerated, unless we regard univer- 
sal notions as not merely real substances, but corporeal. In 
the example given by Aldrich, the so-called Physical definition 
may be regarded as merely an indirect mode of expressing 
the same notion that the Metaphysical definition expresses 
directly. It is thus merely an accidental variation of lan- 
guage, easily reduced to the direct form, and is so regarded 
by Albert, de Prsed. Tract, i. chap. 6. and by Occam, pt. i. 
eh. 26. In all other cases it is no definition at all. 

1 Most Logicians reckon two principal methods of nominal 
definition: 1. by a synonymous term, e. g. " ensis est gladius :" 
2. by Etymology, as ■ in Aldrich's example. The former is in 
fact translation, it being indifferent whether the synonyms 
belong to the same language or not ; the latter will in many 
cases be no definition at all ; a large number of words having 
quite lost their etymological meaning. Neither of these 
methods is countenanced by Aiistotle ; see Appendix, note C. 
The former may be traced to the Greek Commentators ; see 
Alexander, in Metaph. p. 442. ed. Bonitz. The latter is an 
innovation borrowed from the Rhetoricians, by whom it was 
called Notatio. See Cicero, Top. ch. 8. 

" In Mathematics, and in all strict Sciences," says Abp. 
Whately, " the Nominal and the Eeal Definition exactly coin- 
cide; the meaning of the word, and the nature of the thing, 
being exactly the same.'" This remark is based on Locke ; j 
(Essay, b. iii. c. 3. §. 18.) but it confounds the Heal EssenceV 
of Locke, i. e. the unknown constitution of each individual \ 
with the Logical Essence or contents of a general notion. Cf ' 
Zabarello Be Methodis, 1. i. p. 159. 



RUDIMENTA. 41 

Accidentaliter\ Animal bipes implume. Metaphy- 
sice% Animal rationale. Physice, Ens naturale 
constans corpore organico et anima rationali. 

Bonae Definitionis leges potissimum tres sunt. 

1 . Definitio sit adsequata definite : alias non Top. vi. 
explicat definitum. Quae enim angustior est, 
explicat tantum partem, cum definitum sit totum ; 
quae laxior, explicat totum, cum definitum sit 
tantum pars. 2. Ut per se clarior* sit et notior Top.vi.4. 

2, 7. 

^ Accidental definition is composed of genus and one or 
more properties. Accidents properly so called are expressly- 
rejected as useless in definition by Porphyry, Isag. 3. 15. and 
by Boetbius, Opera, p. 3, though admitted by some subsequent 
authorities. Hence animal risibile would be a better example 
than Aldrich's animal bipes implume. But the majority of 
Logicians have very properly regarded accidental definition, 
in any form, as no definition, but merely description. It does 
not analyse the contents of a notion, but enumerates marks 
by which one individual may be distinguished from each other. 
The same notion can have but one definition ; the same indi- 1 
vidual may have many descriptions. Cf. Albert. 1. c. Occam, ' 
pt. i. ch. 27. Wyttenbach. Pracept. Log. p. iii. c. v. §. 14. 
Drobisch, §. 104. 

8 Metaphysical definition, the only proper definition in the 
strict sense of the term, being by genus and differentia, (or 
more correctly by genus and differentim ; see Top. i. 8, 3. 
and supra, p. 24, note s.) it wdll follow, that all definable 
notions must be species. Hence summa genera, which have no 
differentiae, and individuals, which are distinguished only by 
accidents, are not definable. See Arist. Metaph. iv. 3, 6. 
(where for els read ov, supported by two Mss. and by Alexander, 
Schol. p. 693, a. 8.) vi. 15. 2. The supposed difference on this 
point between Aristotle and Locke, or rather Descartes, may 
be reduced to a verbal question. See Appendix, note C. 

* Per se clarior ; i. e. composed of parts greater in extension 



42 ARTIS LOGICiE 

definito : alias non explicat omnino. Dico tamen 

per se, quia pei' accidens potest minus intelligi 

Top. VI. 2. quod notius est sua natura. 3. Ut justo vocum 

fop.vi.2. propriarum'' numero absolvatur : nam ex Meta- 

* phoris oritur ambiguitas, ex nimia brevitate obscu- 

ritas, ex prolixitate confusio. 

j than the definitum, though less in comprehension ; as are the 
I genus and differentia, as compared with the species. For the 
i more universal notions are yvcopLfxarepa cpvaei, though individuals 
! and lower species are yvcopifxarepa r)[juv. See An. Post. i. 2. 5. 
I '^op. vi. 4. 7, 9. 

1 " Vocum jwopriarum ; i. e. words in common use, called in 
Ai.-^Jii.^. the Ehetoric, (iii. 2, 2.) Kvpia ovopLara, i. e. sanctioned by popular 
use; "quern penes arbitrium est et jus et norma loquendi." 
Cf. Poet. 21. 5. Xeyo) he Kvpiov pev cp ;(;pa)i/rat eKaaroi. In the 
Topics, (vi. 2. 4.) they are called established names, {Keipem 
ovopara.^ 






RUDIMENTA. 43 

CAP. II. 

De Propositione Categorica pura, 

§. 1. Secunda Pars Logicse agit de PropositioneH 
sive Enuntiatione ; quod est signum secundae ope-1 
rationis Intellectus, sive Judicium verbis expres- 
sum. 

Quare, ad Propositionem legitimam requiritur. 

1. Quoad vocem, ut sit Or alio affirmans^ e;^/Deint.5.]. 
negans, quae est ejus essentia. 

2. Quoad sensum, ut verum vel falsum significet, Be intA.s. 
(id scil. quod res est, vel secus, dicat,) quod essen- 

* " Sed cum disseramus de Oratione, cujus variae species sunt, 

est una inter has ad propositum potissima, quae pronun- 

ciabilis appellatur, absolutam sententiam comprehendens, sola 
ex omnibus veritati aut falsitati obnoxia : quam vocat Sergius 
effatum, Varro proloquium, Cicero enunciatum, Grseci protasin 

tum axioma; familiarius tamen dUceiuY propositio.'" Apuleius 

de Dogm. Platonis, lib. iii. He has not distinguished between 
dnocpavais and Trpdracrts, — the former of which is rendered by 
Boethius emmciatio, the latter propositio. See Trendelenburg, 
Elem. §. 2. " 'A7r6<pav(Tis quum ad sjllogismum instituendum 
tanquam propositio quae vocatur prsemissa adhibetur, npoTaacs 
dicitur." And so Aquinas, Opusc. xlviii. Tract, de Enunc. 
cap. 1. "Propositio nam solum dicitur de prsemissis ipsius 
syllogismi, sed enunciatio tam de praemissis quam de con- 
clusione." The distinction, however, is not implied in the 
definitions of the two by Aristotle, de Int. 5. 5. and Anal. ^ 
Pr. i. 1 2. 

^ Oratio affirmans, Kardcpaa-is — negans, aTro^ao-is. These are 
literally rendered by Apuleius, Propositio dedicativa and abdi- 
cativa. 



44 ARTIS LOGICiE 

tiae necessario nexum, et proinde proprietas est. 

Unde et 

3. Non est ambigua; sic enim orationes esset. i 

Nee 4. Soloeca vel mutila ; sic enim nihil sig- i 

nificaret. M 

Deiiit.5.5. Quare, ea demum Propositio legitima censebitur, 
Anai.Pr.i. qu8e, juxta definitionem vulgatam, est Oratio Indi- 

cativa'', congrua et perfecta, verum vel f ahum sig- 

nificans, sine amhiguitate. 

§. 2. Ejus Divisiones varise sunt ; 

1. Categorica^ est, quae enuntiat absolute; ut. 
Homo est risibilis. Hypothetica, quae sub con- 
ditione ; ut, si homo est rationalis est risibilis, Vel 
dies est vel nox. 

Quod Categorica dicit, nihilo nexum est ; quasi 
per se subsistens : quod Hypothetica, conditioni 
substat. Unde et haec Divisio peti dicitur a Sub- 
stantia Propositionis ; et per ejus membra respon- 
detur interroganti, Quce est Propositio ? 

Categorica rursus dividitur in Puram et Moda- 
lem^, Hypothetica in Conditionalem, Disjunctivam, 

! « The proposition is defined by Aristotle, \6yos dirocfyapTLKos, 
which is translated by Petrus Hispanus, Oratio indicativa, and 
(better by Boethius, Oratio enunciativa. The rest of Aldrich's 
definition is superfluous. 

^ Categorica. In Aristotle Karrj-yopiKos always signifies af- 
Jirmative, and is opposed, not to vTroderiKos, but to o-reprjTiKos. 
The latter sense probably originated with Theophrastus, who 
first expounded the hypothetical syllogism. See Sir W. 
Hamilton, Ed. Kev. No. 115. p. 221. 

e Aristotle, in de Int. ch. 12. ]. enumerates four modes; 



RUDIMENTA. 45 

&c. Categorica pura, sive Propositio de inesse\ Anal. Pr. 
est quae pure afSrmat vel negat ; i. e. simpliciter r!e int. 12. 

the necessary, the impossible, the contingent, and the possible. 
(avayKOLov — abvvaTov — evhcxojxevov — Svmroi/.) These he afterwards, 
Anal. Pr. i. 2. 1. reduces to two, the necessary and the con- 
tingent. See St. Hilaire's Translation, Preface, p. 66. That 
he adds the true and the false is questionable; the words 
oKrfdis, ovK aXrjdes, in de Int. 12. 10. are perhaps only intended 
to mark the previous four pairs as contradictories, of which 
the one must be true the other false. Subsequent Logicians, 
following the Greek Commentators, have multiplied the 
number of modes ad infinitum. Any adverb annexed to the 
predicate, " homo currit velociter," or even an adjective qualifying 
the subject, " homo albus currit," was regarded as forming a 
modal. The name rporros, as applied both to the modes of 
propositions and to those of syllogisms, is not Aristotelian, 
but comes from the Greek Commentators. (Ammonius, Schol. 
p. 130. a. 16.) 

The post- Aristotelian modes affect the subject or the 
predicate alone, not the relation between them. They are 
thus only pure p ropositions with complex terms, as is 
remarked by Melanchthon, Erotemata Dialectica, p. 132. 
Aristotle's modes affect the copula and the manner of 
thinking, and are psychologically distinct forms of the pro- 
position, as they are rightly treated by Kant, Kritik der r. V. 
p. 71. But in a logical point of view, the distinction of 
modals is unimportant, as not influencing any further process 
of pure thinking. For this reason they are out of place in the 
logical writings of Kant and his followers. See further, 
Prolegomena Logica, note G. 

^ De inesse, — tov vn-apxecv. We find two expressions in 
Aristotle, both of which are sometimes rendered by " being in." 
1. vTrdpxeiv, by which the predicate is said to be in the subject. 

This is equivalent to Karq-yopela-Bai. To A vndpxet navrl roj B =ro 
A KaTrj-yopelTai Kara navros tov B = ^ inest omni B. 2. dvai eV, 

by which the subject is said to be in the predicate. A ianv iv i 
oK(a TO) B = Omne A est B. This is exactly the reverse of | 



46 ARTIS LOGICiE 

(licit Praedicatum inesse, vel non inesse, subjecto 
ut. Homo est animaL Homo non est lapis. M 
dalis, quae cum Modo, h. e. vocabulo experiment 
quomodo Praedicatum insit subjecto ; ut, Necess 
est hominem esse animaL Impossibile est hominem\ 
esse lapidem, De Categorica pura, et quidem sola,| 
impraesentiarum loquor ; de caeteris alibi dicturus. 

Delnt.6.1. 2. ^4^^^^^^^^^^^ ^^^ ^^1^^ ^^P^^^ ^^^^^^i^^ ^^^ '* 

ut. Homo est animal, Non progredi est regredi, 
Negativa, cujus negat ; ut. Homo non est lapis, 
Nullus avariis est dives. Vera, quae quod res est^ 
dicit; Mt, Homo est animaL i^iQ^Zs^^^ quae secus; ut, 

KarqyopelTaL. The English language is defective in not having, 
like the Greek and Latin, a proper copula to express the 
relation of comprehension as well as that of extension. Thus 
the relation expressed by vnapxet and inest can only be strictly 
rendered into English by a circumlocution, " A is a quality 
belonging to B." With the ordinary copula both relations 
must be translated into the language of extension ; t6 A vTrdp- 

Xei ttovtI rw B = All B is A. to A io-riv iv o\(o t« B ;= All A is B. 

The memorable question at issue between Keid and Gillies, 
(see Hamilton on Reid, p. 684.) turns on the above dis- 
tinction. The former uses " being in " as a translation of 
VTrdpx^i'V, the latter, of eV oXm elvai. 

^ KardcfiaaLs icrrcv d7r6(f)av(TLs rivos Kara tivos. ' Anocpao-is iariv 
diTo^ava-Ls tlvos and tivos. Aristotle de Int. 6. 1. " Affirmatio est 
enunciatio alicujus de aliquo. Negatio est enunciatio alicujus 
ab aliquo." Boethius, de Int. p. 332. Aldrich's definition is 
directly applicable only to propositions tertii adjacentis. 

^ Vera — Falsa. This is material, not logical truth and false- 
hood, and admits of no criterion from Logic nor from any 
single science, but only from the proper experience of each 
separate case. But even in this relation Aldrich's definition 
is not quite accurate. Material truth does not consist in the 
conformity of thought with the nature of things per^e; for 



I 



RUDIMENTA. 47 

Homo est lapis, Et cum per hasce species bene 
respondeatur interroganti^ Qualis est Proposition 
(respondent enim per Differentiam et Proprium 
quae in quale prsedicantur) dicuntur hae duag divi- 
siones peti a Qualitate Propositionis. Prior a 
Qualitate Vocis, sive Essentiali ; Posterior a Qua- 
litate Rei, sive Accidentaria. 

3. Universalis^ est quae subiicit terminum com-Deint.7.1. 

. . T . 77 o An. Pr.l. 

munem (cum signo universali, omnis, nullus, &c. i. 2. 
adeoque) pro universis suis significatis distributive 
sumptum. Particularism quae terminum commu- 
nem (cum signo particulari aliquis, quidam, &c. 
adeoque) ex parte tantum significantem. Sin- 
gularis, quae vocem (vel sponte, vel ex signo 
saltern) Individuam ^ ; ut, Socrates legit. Hie 

things are known to us only in their relation to some one or 
other of our faculties. Material Truth consists rather in the 
conformity of the object as represented in thought with the 
object as presented to the senses or to some other intuitive 
faculty. Formal or Logical Truth consists in the conformity 
of thought to its own laws ; and of this, Logic furnishes an 
adequate criterion. 

^ Universal, KaOokov. Particular, iv fiepei, or Kara fxepos. hide- 
finite, abiopiaros. An. Pr. i. 1. 2. Singular, KaO' cKao-rov, (De 
Int. 7. 1.) Omnis is the sign of an universal proposition only 
when taken distributively, as, Omnis homo est animal; when taken 
collectively, as, Omnes Apostoli sunt duodecim, the proposition is 
singular. 

^ Individual names are distinguished as individua signata 
expressed by a proper name, as Socrates : individua demon 
strativa, by a demonstrative pronoun, hie homo; individua vaga 
by an indefinite pronoun, aliquis homo, quidam homo: a dis 
tinction found in the Greek commentators, Schol. p. 148, b 
23 Cf. Albert, de Praedicab. Tract. 4. cap. 7. Aquinas, Opusc 



48 ARTIS LOGICiE 

homo est doctiis. Indefimta\ quae (terminum com- 
munem sine signo, et proinde) ancipitem : nam 
manente formula, vim recipit diversam; ut. Homo 
est animal, nempe omnis: Homo est doctus, aliquis 
scilicet. 

Petitur hsec Divisio a Quantitate Propositionis : 
nempe numero eorum pro quibus subjectum sup- 
ponit : unde et per has species bene respondetur 
interroganti, Quanta sit Propositio ? Hanc doc- 
trinam Scholastici hujusmodi carmine sunt com- 
plexa ; 

Qu(B? Ca. vel Hyp, Quails? Ne, vel Aff. 
Quanta? UnL Par. In, SiiigJ^ 

xlviii. de Int. cap. 7. Of these, the two first will clearly form 
singular propositions. With regard to the last, it has been 
doubted whether they properly form singulai's or particulars. 
Vives maintains them to be singulars ; observing, that quidam 
is not more indefinite than Socrates to one w^ho is not ac- 
quainted with the man. But there is this difference. If 
we say, " quidam concionatur," " quidam legit," there is no 
evidence that the same person is spoken of in the two pro- 
positions ; while Socrates, except by a mere quibble, w^ill always 
designate the same person. There may indeed be two persons 
of the same name ; but in this case the name fails to accora-' 
plish the intended distinction, and we must specify Socrates 
the son of Sophroniscus. Hence aliquis and quidam are pro- 
perly called particulars. Cf. Wallis, Logic, lib. 2. cap. 4. 

1 " The term indefinite ought to be discarded in this relation, 
and replaced by indesignate.'' Hamilton on Eeid, p. 692. 
This proposition has jioclaimj;^ 
the neg^ation of an y lo gical quantity at al L-. 

™ This, and the greater part of the scholastic memorial 
verses, are found for the first time in the SummulcB Logicales 
of Petrus Hispanus, afterwards Pope John XXI. w^ho died in 



i 



RUDIMENTA. 49 

j §.3. Propositio Singularis in Syllogisrno aeque 
potest Universalis Nam Subjectum ejus supponit 
pro omni suo significato. Socrates est homo, Uni- 
versalis est, quia omnis ille Socrates tantum unus 

lest. Indefinitae quantitas judicatur ex materia 
Propositionis, sive habitudine connexionis extre- 

jmorum, quae triplex est; 1. Necessaria'' , quando 

!277. He does not, however, profess to be the author of 
them ; indeed some, including the present, are also noticed 
by his contemporary Aquinas, as established mnemonics. In 
slight measure he has been anticipated by the Greeks. A 
mnemonic for the opposition of modals is found in the synopsis 
attributed to Psellus, and one for the syllogistic moods in 
Nicephorus Blemmidas. But the genuineness of that portion 
of the works of Aquinas has been questioned, and the treatise 
which goes under the name of Psellus is probably a transla- 
tion of the Summulae of Hispanus. The latter work is thus 
our earliest undoubted authority for these curious specimens 
of scholastic ingenuity. See below, p. 82. note z. 

" This is argued at some length in a thesis appended to 
Wallis's Logic ; and is, to say the least, by far the most con- 
venient way of bringing singular propositions under the 
existing rules of the syllogism. At the same time it may be 
remarked that the employment of singular terms as predicates 
is unnatural, and the reasoning, at least in affirmative syl- 
logisms, worthless. See An. Pr. i. 27. 3. Indeed it may be 
questioned whether the eKdeais of Ai'istotle (see below, p. 60.) 
|was regarded by him as a syllogism at all. Cf. Aquinas, 
iOpusc. xlvii. Zabarella, de Quart. Fig. cap. 7. Some 
iadditional remarks will be found in the Appendix, note E. 
I " Aristotle does not recognise this account of matter as 
lunderstood in every pure proposition, but only as expressed in a 
{modal. (See above, p. 44.) In the latter case it is no test of 
[quantity, as there are universal and particular propositions of 
jeach mode. The distinction in the text, however, seems to 



im- \ 
, inj 



50 ARTIS LOGICS 

extrema essential! ter conveniunt ; 2. Contingens, 
quando accidentaliter tantum ; 3. Impossibilis, 
quando essentialiter difFerunt. Unde Propositio 
Indefinita pro Uiiiversali habetur in materia im- 
possibili et necessaria ; pro Particulari vero 
contingenti. 

Quare^ Quantitas Propositionis, quatenus ad 
Syllogismum facit, est duplex : Universalis et 
Particularis, Et nota, quod Universalis affirmans 
symbolura habet A ; negans E : Particularis affir- 
mans symbolum I ; negans O. 

Asserit A; negat E: Universaliter amhce. 
Assent I; negat O: sed Particular iter amho^. 

have been early introduced. It is implied in the commentary 
of Ammonius on de Int. 7. (Scholia, p. 115. a. 14.) And 
Petrus Hispanus defines the three kinds of matter thus; 
Necessary, when the predicate is of the essence, or a property : 
contingent, when it is an accident to the subject; impossible, 
when a repugnant quality. In this point of view, the sup- 
posed criterion of quantity is inapplicable to propositions in 
which the predicate is an inseparable accident. But the 
whole question of matter is clearly extra-logical. See Sir W, 
Hamilton, Ed. Rev. No. 115. p. 217. The Logician cannot 
determine a proposition to be necessary or contingent, unless 
stated as such. The point must be ascertained from the Science 
to which the proposition materially belongs. The Logician, 
however, may use indefinites as particulars, not assigning a|j 
quantity from the matter, but admitting an indefinite premise-'" 
(and therefore conclusion) where the rules of the figure do nofc 
require an universal. Hence the minor premise in fig. 1 . may 
be indefinite, but not the major. See An. Pr. i. 4. 9. 

p On these lines Wallis remarks, " Non tam erant solicit! 
de syllabarum quantitate, aut syntaxeos ratione, quam ut 



I 



RUDIMENTA. 51 

In Universalis signum affirmans distribuit tantum 
Subjectum^: Negans, etiam Praedicatum. Nam ut 
verum sit Omne a est h, sufficit aliquod h con- 
venire omni a: sed falsum est nullum a esse b, si 
vel aliquod h conveniat alicui a, Eodem argu- 
ment o, ut sit verum Aliquod a est h, sufficit si vel 
aliquod b conveniat alicui a : sed falsum est quod 
aliquod a non est b, nisi illud a difFerat a quo vis 5/ 
Et proinde 

In particulari, nuUus terminus distribuitur, praeter ^ 
negantis prjedicatum, quod semper distribuitur. 

Quanquam igitur fieri potest, ut pra^dicatum 
distribuatur in affirmante, tamen non est neces- 
sarium ; sed per accidens fit, et virtute significati, 

Rhythmus constet aut SfioioTeXevrov. Alii tamen, quo constet 
versus, pro sed universaliter, substituunt verum generaliter ; et, 
quo Syntaxi prospiciatur, pro amho, neglecto Rhythmo, sub- 
stituunt amh(e ; respicientes vocem subintellectam, propo- 
sitiones." 

•» In opposition to this, the almost unanimous doctrine of 
former Logicians, the New Analytic of Sir William Hamilton 
is founded on the principle that both terms in every propo- 
sition have a determinate quantity always understood in 
thought, and which ought to be expressed in words. Of the 
truth and value of this addition to the ordinary logical forms 
there can be no question; but its systematic introduction 
into the present work would not be possible without a com- 
plete rewriting of Aldrich's text. 

r Aldrich assumes the distribution of the predicate in a 
negative, to prove the simple conversion of E. Those who 
adopt Aristotle's proof of the latter, (see below, p. 60.) might 
deduce the former from it. Both however may fairly be 
allowed to stand on their own evidence. 

E 2 



52 ARTIS LOGIC.E 

non lurtute signL In statuendis autem Proposi- 
tionum legibus, spectandum est id tantum, quod 
structura postulate non quidquid sensus admittit : 
cum illud essentiale, et perpetuum sit ; hoc muta- 
bile, et incertum. 

Haec igitur regula generalis esto, quod in Pro- 
positione A, subjectura tantum distribuitur ; in O, 
tantum Praedicatum; in I,neutrum; in E,utrumque. 

§. 4. Propositionibus^ accidunt Oppositio et 
Conversio. Opponi dicuntur duse, quae, cum sub- 
jecta habeant et praedicata omnino eadem, Quan- 
titate tamen, vel Qualitate vocis, vel utraque 
pugnant. 
Deint. 7. Oppositiouis* doctriua tota colligitur et demon- 

Anal. Pr. 

s Opposed Propositions, — dvriKeifxeuai Trpordo-eis, Arist. a term 
sometimes limited to Contradictories. 

t As Logic can take no cognisance of widerstood matter, the 
•' necessary, impossible, and contingent " should be omitted from 
the table of Opposition. It is no part of the province of the 
Logician to determine when a given Proposition is materially 
true or false ; but only what formal inferences may be made 
upon the assumption of its truth or falsehood. Hence the 
Canons of opposition should be expressed only in the hypo- 
thetical form. They may be briefly given thus : 
\. If A is true ; O is false, E false, and I true. 

2. If A is false ; is true ; E and I unknown. 

3. If E is true ; I is false, A false, and O true. 

4. If E is false ; I is true ; A and O unknown. 

5. If I is true ; E is false ; A and O unknown. 

6. If I is false ; E is true, O true, and A false. 

7. If is true ; A is false ; E and I unknown. 

8. If is fciel ^A is. true, I true, and E false. 
So that from the truth of an universal, or the falsehood of a par- 



II. 1^. 



1 



RUDIMENTA. 



53 



stratur ex apposite Schemate, in quo, A. E. I. O. 

sunt quatuor Propositiones quantitate sua et quaii- 

tate signatae ; quae 

sunt V. f. (hoc est, 

vercBYelfalsce) pro 

materia n, i. c, 

(hoc est, necessaria, 

impossihili, contin- 

genie ;) quod ex 

ipsa materise defi- 

nitione satis patet. 

De necessaria; quia 

Propositionis ex- 

trema in ea essenti- 

ahter conveniunt : 

de impossibili; quia 

in ea essentiahter differunt : de cont'ingenti ; quia 

secus non esset materia contingens. Inspecto 

igitur hoc Schemate facile est 

1. Oppositionist species numerare ; quae sunt 

ticular, we may infer the accidental quality of all the opposed 
Projiositions ; but from the falsehood of an universal, or truth 
of a particular, we only know the quality of the Contradictory. 
* Contradictory, dvTi(f)aTiKa)s (avriKeiixevai). Contrary, evavricos. 
Arist. The term Siihcontrary {vnevavrioos) is not used by Aristotle 
to denote the opposition of particulars ; though he admits the 
opposition itself, de Int. ch. 7. In Anal. Prior, ii. 15. he calls it 
an opposition Kara rrjv Xe^tv, but not Kar dXrjdeiav. The term is 
used by the Greek commentators, (Ammonius, Schol. p. 115. 
a. 15.) followed by Boethius, Int. ad Syll. p. 564. Subaltern 
propositions {InaKXriXoi) are not noticed at all by Aristotle. 
The laws of subaltern opposition are first given by Apuleius, 



n. V. 




f. n. 


i. f. 


A. Contrariae E. 


V. i. 


c. f. 




f. c. 


a- 
?8 


V 


g 

Is 


n. V. 




f. n. 


i. f. 


I. SubcontrariEe 0. 


V. i. 


C. V. 




V. c. 



54 ARTIS LOGICS 

vulgo quatiior : Contradtctoriay Contraria, Subcon- 
traria, Subalterna. 

2. Singularum definitiones conficere. V. g. Oppo- 
s'Uio Contradict or ia, est inter (A. O. vel E. I. hoc 
est) duas Categoricas quantitate pariter et qualitate 
pugnantes, Contraria, inter (A. E. h. e.) duas 
universales qualitate pugnantes &c. 

3. Oppositarum Canones quatuor eruere et 
demonstrare hunc in modum. 

1. Contradictoriae A. O. vel E. I. sunt in nulla 
materia simul verae ; in nulla simul falsae ; sed in 
quacunque una vera, falsa altera. 
Soph. Sed notandum est, ad Contradictionem requiri 

Elench. -, . -, 1 -, 7 7 ' 

5.5. quatuor: nempe ioqui de eodem 1. eodem modo, 

2. secundum idem. 3. ad idem, 4. in eodem tempore"^; \ 
quarum conditionum si defuerit aliqua, possunt ! 
Est et Non est inter se bene convenire. E. g. ! 
1. C'adaver hominis est et non est homo : Est enim : 
homo mortuus ; Non est homo vivus. 2. Zoilus"". ^ 

De Dogmate Platonis, lib. 3. though he does not give it a 
name. He is followed by Marcianus Capella. The name is 
given by Boethius, Intr. ad Syll. p. 566. and in the Com- 
mentary on the De Interpretatione. The treatise of Apuleius, 
if genuine, is a production of the second century, contemporary 
with, or a little prior to, the works of Alexander of Aphrodisias. 
The three first kinds of opposition are called by him AlterutrcB, 
IncongrucB, and Suppares. 

" Secundum idem, ad idem. Cf. Plato, Eep, iv. p. 436. 
ArjXov oTi ravTov Tavavria noieiv rj Trdaxeiv Kara ravrov ye Ka\ Trpos 
ravTov ovK iOekqaei a^a. ; 

V Zoilus, see Martial, lib. xii. ep. 54. 

Crine ruber, niger ore, brevis pede, lumine lapsus, 
Bern magnam prsestas, Zoile, si bonus es. ^ 



I 



RUDIMENTA. 55 

est et non est niger : I]st enim crine ruber, niger 
ore. 3. Socrates''' est et non est comatus : nempe 
est, ad Scipionem, non est, ad Xenophontem com- 
paratus. 4. Nestor est et non est senex : Est 
enim, si de tertia ejus astate, non est, si de prima 
loqueris. 

2. Contrarise A. E. in nulla simul verse ; in 
Contingenti, simul falsae ; in ceteris, una vera, 
falsa altera ; nempe in Necessaria, vera A. falsa 
E ; in Impossibili, vera E. falsa A. 

3. Subcontrarise I. O. in Contingenti, simul 
verae ; in nulla simul falsae ; in Necessaria, vera I. 
falsa O ; in Impossibili, vera O. falsa I. 

4. Subalternae A. I. vel E. O. et simul verae, et 
simul falsae, et una vera, falsa altera esse possunt. 
Nam in Necessaria, simul verae sunt A. I ; in 
Impossibili, simul verae E. O ; in eadem, simul 
falsae, A. I. et in Necessaria, simul falsae E. O ; 
in Contingenti, (propter A. E. falsas, I, O. veras) 
A. I. vel E. O. sunt una vera, falsa altera. 



" Aldrich has not before mentioned the opposition of 
singulars. " Socrates is wise," " Socrates is not wise." These 
are contradictories; though the definition does not strictly 
include them, having inadvertently been worded solely with 
reference to universals. But they have the essential feature 
of contradictories, that one is always true, and the other false; 
(de Int. 7, 8.) and the definition given. Anal. Post, i 9. 6. will 

include them : — 'Ai/rt^ao-ts 8e dvTiOfo-is ^s ovk eart fiera^v KaB" avrrjv. 

Some Logicians call the opposition of singulars, secondary con- 
tradiction. Boethius, p. 613, regards them as contradictories. 
See also Wallis, lib. ii. cap. 5. 



56 ARTIS LOGICS 

Possunt etiam aliter hi Canones Oppositarum, 
cum pluribus aliis, turn hoc quoque modo demon- 
strari. 

1. Contradictoriae A. O. vel E. 1. nee simul verce 
nee simul falsce esse possunt. Quod enim una 
negat, idem altera de eodem, secundum idem, 
affirmat : Id vero fieri nee natura patitur, nee 
sensus ipse communis. Quare, 

a. Si Universalis vera sit. Particularism quae sub 
ea continetur, vera est. Et 

/8. Si Particularis falsa sit. Universalis, quae eam 
continet, falsa est : Quoniam enim Subjectum in 
Universali distribuitur, fit, ut in ea, et in Particulari, 
idem, de eodem, secundum idem, dicatur : vere 
igitur et falso simul dici, (hoc est, affirmari simul et 
negari) nequit. 

2. Contrariae A. E. non possunt esse simul verce : 
sed in materia contingenti sunt simul falser. Nam 
F. Exponatur Universalis vera ; Ergo particularis 
vera per 1, «; Ergo quae particulari contradicit 
falsa per 1. Sed base est Expositae contraria. 

2^ Exponatur Universalis de materia contin- 
genti ; Ergo et haec falsa est, et Particularis vera, 
vi materia : Ergo quae particulari contradicit falsa 
per 1. Sed haec est Expositae Universali con- 
traria. 

3. Subcontrariae I. O. simul falsce esse non pos- 
sunt : sed simul verce, vel una vera, falsa altera, 
esse possunt. Sunt enim duae duarum Contra- 
riarum Contradictoriae, ut in Schemata patet, cum 



RUDlMEiNTA. 57 

contrariis decussatim comparandse. Quare, (per 1. 
et 2.) Subcontrariag sunt in nulla materia simul 
falsce; quia contrarise in nulla simul verw : Sub- 
contrariae in contingenti simul verse ; quia Con- 
trariae in eadem simul falsse. In Impossibili vero, 
et Necessaria, eadem utrisque lex est, ut sit una 
vera, falsa altera. 

4. Subalternae A. I. vel E. O. et simul verce, et 
simul falsce, et una vera, falsa altera esse possunt. 
Nam 1 ^ Si subalternans (nempe Universalis) vera 
sit, Subalternata (sive Particularis) vera est (per 1. 
a.) 2^. Si Subalternata falsa. Ergo Subalternans 
falsa (per 1. /3.) 3^ Si Subalternans falsa. Ergo 
quae illi contradicit vera (per 1.) Ergo hujus 
Subcontraria, quae est Expositae subalternata, vera 
vel falsa esse potest (per 3.) 4^ Si Subalternata 
vera. Ergo quae illi contradicit falsa (per 1.) Ergo 
hujus Contraria, quae est expositae Subalternans, 
vera vel falsa esse potest (per 2.)'' 

X On the doctrine of Opposition in general, it may be 
remarked, 1. That Subalterns are improperly classed as 
opposed propositions, and should be referred to a separate 
table as immediate inferences. 2. That the Greek expressions 
Tras — ov nas, ovbiis — eVrt ris, are better adapted to signify the 
relations both of opposition and of immediate inference than 
their ■ English substitutes, all, none, and some. Some men is 
naturally understood as meaning more than one, whereas 
not all men includes one or any number short of the whole. 
Hence the Aristotelian examples, ivas avOpccnos XevKos, ov nds 
avdpanos XevKos, express a complete contradiction more accu- 
rately than all men are white, some men are not white; as the 
latter admits of a third possibility, one man is not white. 



58 ARTIS LOGICS 

An. Pr. I. §.5. CoNVERTi dicitur Propositio, cujus extrema 
transponuntur^ Variis id modis fieri potest, sed 
praesertim duobus^: 1. Slmpliciter, quando tarn 



3. That there may be material as well as formal consequences 
in opposition and immediate inference, as well as in mediate 
inference. Thus, all men are white, all men are black, are 
materially, but not formally, contrary to each other. A is 
greater than B, therefore B is less than A, is a material imme- 
diate inference. The formal consequences alone come under ■ 
/the cognisance of Logic. 

y The logical, as distinguished from the grammatical pro- 
position, is properly of the form distinguished as tertii 
adjacentis, and the copula is always in the present tense. 
For Logic considers words only as the signs of thought ; and 
the copula indicates the present union of two notions in the 
mind of the thinker, not the past or future connection of 
facts narrated or predicted. Every proposition should there- 
fore, before conversion, be stated in the form A is B, which 
by conversion becomes B is A, with a change, if necessary, 
in the quantity. To give more minute directions would be 
to encroach upon the province of the Grammarian : we must 
be guided by the idiom of the language we are using. In 
Latin, e. g. the substantive acquires an adjective power, and 
the adjective a substantive, without change of form ; e. g. 
"nullus sapiens est iracundus," " nullus iracundus est sa- 
piens." In English we must say, " No angry man is wise." 
Eules on this point are extra-logical. 

The directions of some Logicians as to the conversion of 
past and future time, e. g. "nullus senex erit puer," are also, 
logically speaking, out of place here, though practically helps 
to a beginner. For these tenses not being logical copulse, the 
sentence is not, as it stands, a logical proposition; and should 
be reduced to such, before it comes into the hands of the 
converter. 

^ Aristotle's account of conversion differs somewhat from 
this. He divides conversion into universal and particular, 



RUDIMENTA, 59 

quantitas, quam utraque qualitas servatur. 2. Per 
accidens^, quando servata qualitate, quantitas 
mutatur. 

f Ec I Simpliciter convertitur Ev A per Acci^ et 
conversio utrobique illativa est. 

according to the quantity of the proposition after conversion. 
Consequently E is converted universally, A and I particularly. 
He does not recognise any conversion of O. Simple con- 
version, {dnX^ dvTi(TTpo({)r},) is mentioned by Philoponus, Scholia, 
p. 148. b. 21. Boethius uses the terms generalis and per ac- 
cidens. In the system of Sir W. Hamilton, by assigning a 
quantity to the predicate of every proposition, the various 
kinds of conversion are reduced to that of simple conversion 
alone. 

^ Per accidens; so called because it is not a conversion 
of the universal per se, but by reason of its containing the 
particular. For the proposition " Some B is A," is primarily 
the converse of " Some A is B," secondarily of " All A is B." 
Se^ BoetMus, de Syll. Cat. p. 589. 

^ A St U, p>^f contra ; sic Jit conversio tota. 

Conversion by contraposition, which is not employed 
by Aristotle, is given by Boethius in his first book, De 
Syllogismo Categorico. He is followed by Petrus Hispanus, 
who first gives the mnemonic, as above. It should be ob- 
served, that the old Logicians, following Boethius, main- 
tain, that in conversion by contraposition, as well as in 
the others, the quality should remain unchanged. Con- 
sequently the converse of "All A is B" is "All not B is 
not A," and of " Some A is not B," " Some not B is not 
not A." It is simpler, however, to convert A into E and O 
into I, (" No not B is A ;" " Some not B is A,") as is done by 
Wallis and Abp. Whately; and before Boethius by Apuleius 
and Capella, who notice tlie conversion, but do not give it a 
name. The principle of this conversion may be found in 
Aristotle, Top. ii. 8. 1. though he does not employ it for 
logical purposes. 



60 ARTIS LOGlCiE 

Nam 1. sit vera E% puta Nullum A est B : Ergo 
(cum uterque terminus distribuatur) quodvis A 
difFert a quovis B. Ergo vicissim ; Ergo Nullum 
B est A. 2. Sit vera I : Ergo falsa est ejus Con- 
tradictoria E : Ergo et contradictorise simpliciter 
conversa : Ergo quae conversae contradicit, (i. e. 
expositae simpliciter conversa,) est vera. 3. Sit 
vera E. Ergo et ejus simpliciter conversa : Ergo 
et conversae subalternata : quae est expositae con- 
versa per accidens. 4. Sit vera A ; Ergo et ejus 

*= Sit vera E. This is the proof given by Theophrastus 
and Eudemus. (Alexander, SchoUa, p. 148. b. 29.) Aristotle 
proves it by the method called cKdeans, i. e. by the exhibition 
of an individual instance, (jKriOevat, exponere sensui ; whence a 
syllogism with singular premises is called syllogismus eocpo- 
sitorius.) Thus, No A is B, therefore No B is A, for if not, 
Some individual B, say C, is A. Then C is both A and B, 
and therefore it will not be true that No A is B ; which was 
the original proposition, i^ristotle does not assume the con- 
version of I to prove that of E, which would be arguing in a 
circle. For a fuller account, see Hamilton on Eeid, p. 696. 

Alexander himself offers a third proof by syllogism in the 
first figure. No A is B, therefore No B is A ; for suppose 
" Some B is A," and " No A is B," .*. Some B is not B. 

Having proved the conversion of E, those of A and I will 
follow from it. " All A is B, therefore Some B is A ;" or else 
No B is A, and therefore (by conversion) No A is B ; whereas 
we assumed All A is B. And again. Some A is B, therefore 
Some B is A ; or else No B is A, and therefore No A is B. 

For these proofs, the only assumption necessary is the 
principle of contradiction. But proof of any kind is super- 
fluous. Conversion and other immediate inferences are 
necessary results of the laws of thought, equally evident 
and more direct than the mediate inferences by syllogism. 
Neither process is dependent on the other. ^ 



RUDIMENTA. 61 

subalternata : Ergo et subalternatae simpliciter 
con versa : quae est expositae per Accidens^. 

Ceterae Conversiones% cum sint partim ambiguae, 

d In Conversion, as in Opposition, Singular Propositions 
have been neglected by Aldrich. Concerning these, the 
following extract from Wallis may assist the learner. " Pro- 
positio Singularis, (sive Affirmativa sive Negativa,) cum semper 
Universalis sit, observat leges aliarum Universalium. Puta, 
Virgilius est Poeta ; ergo Aliquis Poeta est Virgilius. Item, 
Virgilius non est Grmcus ; ergo Nullus Grcecorum est Virgilius. 
Atque in aUis similiter. 

" Si autem Convertendee proposition is Prcedicatum sit Indivi- 
dmim, (quodcunque habuerit Subjectum,) Convertentis Suhjectum 
(quippe quod fuerat Convertendce Prcedicatum) Individuum erit ; 
propterea et Propositio Convertens (siqua sit) necessario erit 
Singularis, adeoque Universalis.''' See also Reid's Works, ed. 
Hamilton, p. 697. 

® C(Bter(B conversiones. For the benefit of the curious, we 
quote the following : " Tres igitur sunt famosae apud Logicos 
conversionis species. Dico famosae, quoniam nonnulli mo- 
derni invenerunt duas alias conversionis species, quarum una 
est conversio propositionum nullius quantitatis, ut exclusivae 
et reduplicativae. Nam sic convertitur exclusiva ; tantum 
homo est rationalis, omne rationale est homo : reduplicativa 
autem sic convertitur : homo in quantum homo est rationalis, 
rationale est homo in quantum homo. Item propositionum 
modalium, ut hominem esse album est possibile, ergo pos- 
sibile est hominem esse album. Item alii imaginati sunt 
duas alias species. Prima est quando mutatur qualitas et 
non quantitas, ut hie ; omnis homo est animal, omne animal 
non est homo. Secunda est quando mutatur quantitas et 
qualitas, ut hie ; omnis homo est animal, aliquod animal non 
est homo. Verum quia hujusmodi conversiones non sunt in 
usu, nee nobis deserviunt pro reductione syllogismorum, ideo 
immorabimur circa primam et secundam speciem, tangentes 
breviter de tertia, omnibus aliis relictis." Javellus, de Pro- 
positione, cap. ii. 



62 ARTIS LOGICiE 

partim falsae, partim ad praecepta Syllogismorum 
in utiles, in Logica negliguntur^ 

' Is the converse an inference from the exposita, or, as 
Whately says, the same judgment in another form? This 
was an early point of dispute among the Schoohnen. See 
Albert, in Anal. Pr. Tract, i. cap. 8. Aristotle clearly considers 
it an inference; otherwise it would be absured to prove it. 
Eeid, in his Account of Aristotle's Logic, defines it as an 
inference, and the definition is accepted by his learned Editor. 
Kant, too, regards both conversion and opposition as syllogisms 
of the understanding, the new judgment being always different 
in form, though not in matter, from the old. As regards con- 
version per accidens, the exposita is clearly not identical wdth 
the converse ; as it cannot be substituted for it, but may be 
false, while the converse is true. But on the new system of 
Sir W. Hamilton, the predicate being quantified, and the 
proposition reduced to an equation between the terms, it is 
better to consider the converted proposition as identical with 
the exposita. 



RUDIMENTA. 63 

CAP. III. 

De Syllogismo Categorico pura, 

§. 1. Tertia pars Logicae agit de Argumento'' 
sive Syllogismo, quod est signum tertiae opera- 
tionis intellectiis : nempe Discursus, vel Ratioci- 
nium Propositionibus expressum. 

Quare, cum Discursus^ sit progressus mentis ab 
uno judicio ad aliud^ perspicuum est in eo requiri 
1. Aliquid unde discursus ordiatur. 2. Aliud quo 
perveniat. 3. Ea sic ab invicem pendere, ut unum 
ex alio, et alius vi innotescat ; secus enim, unum 
post aliud cognoscere, est tantum saepe judicare. 

Jam^ ex quo aliud cognoscendum est, ipsum Anal. Post. 
certe praecognosci debet ; et proinde quasi sine 
discursu notum, antecedere, poni, prcemitti : et ex 
eo reliquum concliidi, colligi, inferri et seqtd dicitur. 
Est autem duplex consequentia : 

1. Materialis ; quando ex Antecedente Conse- 

quens infertur, sola vi Terminorum% quae est 

* Argument is not properly synonymous with syllogism, but 
with the middle term only. See Ed. Rev. No. 115. p. 218. 

^ See before, p. 5. note k. 

^ The force of the terms leads to a conclusion by suggesting 
to the mind certain additional truths concerning the things 
spoken of, which are not given in the premises. But this 
additional knowledge is clearly extralogical. See Appendix, 
note D. The m.atter of the syllogism is all that is given to 
and out of the act of reasoning : the form is what is conveyed 



64 ARTIS LOGICS 

Argumenti materia: ut. Homo est animaL Ergo 
est vivens. 

2. F or malts ; quando infertur propter ipsum 
colligendi modum, quae est argumenti forma; 
vX, B est A, C est B. Ergo C est A, Mutatis 
terminis et servata eorum disposition e, Materialis 
plerumque fallit, Formalis semper obtinet : et 
proinde haec solum in Logica spectatur, ilia, tan- 
quam mutabilis et lubrica, negligitur. 
Anal. Pr. Hisce iutellectis, opinor satis constare quo sensu 
Top.i.1.2. definiatur Syllogismus ; ^ Oratio in qua positis qui- 

in and by the act itself. The former is expressed in the terms 
of which the reasoning is composed, and which vary in every 
different act of thought; the latter appears in the relation in 
which those terms are thought to one another, as constituting 
premises which necessitate a conclusion. This remains within 
certain fixed limits in every different act of thought. The 
same principle of distinction may be applied to discern 
between the matter and form of concepts and judgments. 
The logical forms of the syllogism are exhibited in mood and 
figure, as those of the proposition in quality and quantity. 
Cf. Burgersdyck. Inst. Log. 1. ii. c. 6. " Forma syllogismi est 
apta trium propositionum dispositio ad conclusionem ex 
praemissis necessario colligendum. Haec aptitudo posita est 
in figura et modo." A distinction slightly varying from the 
above will be found in Crakanthorpe, Logica, 1. iii. c. 13. and 
another in Kant, Logik, §. 59. The latter has been censured 
by Krug, Logik, §. 72. 

d Arist. Anal. Pr. i. I. 6. SuXXoyior/xos be eVrt \6yos iv a TeOevTOiV 
TLpav erepov Ti rav Keijievcov e^ dvdyKrjs (TVfx^aivei ra ravra eivai. See 

also, Top- i. 1. 2. The latter definition is translated by 
Aulus Gellius, xv. 26. " Oratio in qua, consensis quibusdam 
et concessis, aliud quid, quam quae concessa sunt, per ea, 
quae concessa sunt, necessario conficitur." The word concessis 



RUDIMENTA. 65 

busdam atque concessis, necesse est aliud evenire 
prwter^et propter ea quce posita sunt atque con- 
\ cessa, 

I §. 2. MuLTiE sunt ejus species; sed una tantum 
praesentis instituti ; nempe Categoricus simplex, 
i. e. qui constat tribus Propositionibus de inesse". 
E quibus duas priores sunt Antecedens, tertia 
Consequens; quae extra Syllogismum spectata 
(scil. quamdiu haeret in incerto) Prohlema\ etAnai. Pr. 
Qucestio^ dicitur ; in Syllogismo autem (nempe l 26. i*. 
post fidem factam) Conclusio, Quaestionis duoiLi". i. 
sunt extrema, Subjectum et Prasdicatum ; quorum 
de Convenientia vel Dissidio inquiritur, ope termini 

is too limited ; being strictly true only of the topical syllogism. 
Of. Trendelenburg, Elementa, §.21. On the charge of petitio 
■principii, sometimes brought against the syllogism, see Ap- 
pendix, note E. 

® i. e. pure Categoricals. 

^ To yap avTO yevei Trpo^Xrjixa kol Xripfia kol 6}xo\6yqpLa kol crvfi' 
Trepao-jxa Koi d^ico/xa* navra yap TTporaaeis rfj cr)(e(T€L Tr)v 8ia(f)opau 
exovra' npoTidepevov yap els Se'i^iv ois pr] yvoopipov tt p 6 ^Xrj pa KaXeirat, 
Xap^avopevov de els aXkov del^cv Xrjppa Ka\ opoXoyqpa' a^iatpa be 
orav akrjdes fj koi e^ eavrov yvatpipov, dedeiypevov 8e av pire pacr pa. 
Alexander, Schol. p. 150, b. 40. This accords with the sense 
of Trpo^Xrjpa in Anal. Pr. i. 4. 15. i. 26. 1. The dialectical use 
of the term in disputation is not very different. Cf. Topics, 
i. 4. I, 3. i. 11. 1. Schol. p. 256, a. 14. 

8 Qucestio ; to Cn^ovpevov, Anal. Post. ii. 1. 1. which term, 
however, has a more extensive application than is here 
assigned ; for two of the Qucestiones Scibiles, an sit and quid sit, 
cannot in all cases be determined syllogistically. See An. 
Post. ii. 3. and Appendix, note C. 

F 



66 ARTIS LOGICS 

alicujus tertii ; idque propter Canones sequentes% 
in quibus vis omnis Syllogistica fundatur. 

1. Quae conveniunt in uno aliquo eodemque 
tertio, ea conveniunt inter se. 



^ These Canons are an attempt to reduce all the three 
figures of syllogism directly to a single principle ; the dictum 
de omni et nullo of Aristotle, which was universally adopted 
by the scholastic Logicians, being directly applicable to the 
first figure only. This reduction, so long as the predicate 
of propositions has no expressed quantity, is illegitimate; 
the terms not being equal, but contained one within another, 
as is denoted by the names major and minor. Hence, as 
applied to the first figure, the word conveniunt has to express, 
at one and the same time, the relation of a gi^eater to a less, 
and of a less to a gi-eater, — of a predicate to a subject, and of 
1 a subject to a predicate. In the system of Sir W. Hamilton, 
sby assigning a quantity to the predicate, the terms of every 
proposition are equal in extent; and the Canons become 
legitimate representatives of the syllogism; but in this case 
they are only narrower statements of the true syllogistic laws ; 
which are given in the Principles of Identity and Contra- 
diction. (Every A is A; No A is not A.) These, with the 
Principle of Excluded Middle, (Every thing is either A or 
not A,) are the highest and most exact statements of the 
Necessary Laws of Thought. Cf. Prolegomena Logica, p. 2'23. 
Wallis mentions the Canons as recent innovations in Logic. 
" Nonnulli autem Logici, (nostri seculi aut superioris,) post- 
habita veterum probatione per Dictum de Omni et de Nullo, 
aliud substituunt illius loco Postulatum ; nimirum, Quce con- 
veniunt in eodem tertio conveniunt inter se. Inst. Log. 1. iii. c. 5. 
Cf. Bacon. Nov. Org. 1. ii. aph. 27. Melanchthon {Erotemata, 
p. 172.) mentions them as adopted by a sect of Logicians in 
his day. The earliest wi'iter to whom I have found them is 
Eodolphus Agricola, De Inv. Dial. i. 2. He describes at con- 
siderable length the office of the middle term as a measure of 
equality or inequality. 



RUDIMENTA. 



67 



2. Quorum unum convenit, alterum differt uni 
et eideixi tertio, ea difFerunt inter se. / 

3. Quae non conveniunt in uno aliquo eodemque / 
tertio, ea non conveniunt inter se. 

Sunto enim A et C, nee assignari possit ejusmodi 
tertium. Ergo nihil babent commune ; Ergo non 
conveniunt inter se. 

4. Quorum neutri inest quod non sit in alio, ea\ 
non difFerunt inter se'. , 

5. Quae non probantur convenire in uno aliquo j 
eodemque tertio, ea non probantur convenire inter 1 
se. Dubitari enim potest utrum detur ejusmodi 
tertium, et dubitatio ista non toUitur. 

6. De quibus non probatur, convenire unum 
eidem alicui tertio cui alterum differt, ea non 
probantur difFerre inter se. Dubitari enim potest, 
utrum detur ejusmodi tertium, h. e. utrum alterutri 
insit quod non est in reliquo ; et dubitatio ista non 
tollitur^. 

* The third and fourth Canons relate to conditions under 
which no syllogism can exist. " Two things, which have not 
a point in common, are totally distinct." " Two things, which 
have not a point of difference, are undistinguishable." But if 
there is no such point, there is no middle term, and therefore 

I no syllogism. 

^ The fifth and sixth Canons relate to conditions under 

I which no syllogism does exist. "If no point has been 

! assigned, whether of agreement or difference." But if so, 

I there is no syllogism. 

I Hence these four cannot be called Canons of syllogism. 

j They may be useful, however, for examining the illogical 

j positions of an opponent. 

f2 



68 



ART IS LOGICJ£ 



§. 3. Ex sex hisce Principiis Syllogismi struc- 

tura sic deducitur. 

Anal. Pr. 1. In oiiini Syllogismo sunt tres, et tres tantum, 

termini. Nam Syllogismus^ omnis probat aliquam 

conclusionem : Et in ilia sunt duo tantum extrema : 

Et ilia neque convenire, neque difFerre probatur, 

sine uno, unoque tantum, tertio. 

Anai.Pr.i. Jam, Prasdicatum Quaestionis dici solet majus 

1.6.1.1.5.7. extremum^ , major terminus; Subjectum Quaestionis, 

Anai.Fr. I. minor : Terminus vero tertius, cui quaestionis 

38.8.1.4.3. . ^ 

1.5.1.1.6.1. extrema comparantur, Aristoteli Argumentum, 
vulgo Medium'^: Nam Praedicatum Quaestionis 
plerumque amplius est Medio ; hoc minori. 

^ Aristotle adopts an inverse method ; first examining the 
structure and stating the laws of each separate figm-e of 
syllogism, in An. Pr. i. ch. 4, 5, 6. and afterwards enumerating, 
as the result of the examination, the general laws applicable to 
all, in An. Pr. i. 23 sqq. On the respective merits of the two 
methods, see Pacius on An. Pr. i. 4. Reid, ed. Hamilton, p. 700. 

^ Majus extremum ; to yt-el^ov aKpov, (also to TrpwTov, An. Pr. i. 
31. 2.) minus; t6 eXaTTov, (also to eaxaTov, An. Pr. ii. 8. 3.) 
Terminus, 6pos, for the various meanings of which, see Waitz, 
vol. i. p. 370. Major term; fielCcovopos: minor; eXarrcoj/ opos, An. 
Pr. i. 5. 7. The definitions of the major and minor t^rms 
given in the text are condemned by Pacius, (on An. Pr. i. 7.) as 
inapplicable to the indirect moods. Aristotle gives a separate 
definition of the three terms in each figure. But the indirect 
moods may, without loss, be dispensed w^ith. An account 
of various theories of the distinction between the major and 
minor term will be found in Sir W. Hamilton's Discussions^ 
2d Ed. p. 670. Aldrich's prcsdicatum qucestionis corresponds to 
the distinction maintained by Alexander and Averroes. 

" More correctly, " Aristoteli medium, Ciceroni aliisque argu- 
mentumS' See Ed. Rev. No. 115. p. 218. The nearest Greek 



\ 



I 



RUDIMENTA. 69 

2. In omni Sylloffismo sunt tres, et tres tan turn, Anai.Pr.i. 

. . M Ti/r T 23.5.1.25. 

propositiones. Duae praemissae", in quibus Medium 8. i. 32. 8. 
cum extremis seorsim conferatur, (nempe Major, Auai. Pr. 
in qu^ cum majori; Minor, in qua cum minori ;) 
una Conclusio, in qua extrema invicem commit- 
tantur. 

N.B. ]. Quod Major dici solet simpliciter Pro- 
positio ; M'mor , Assumption . 2. Quod Medium non 
ingreditur conclusionem, alias idem per idem pro- 
baretur : adeoque non essent tres termini. 

3. Ancipiti medio nihil conficitur. Neque enim/^nai. Pr. 
afFertur in hoc casuunum aliquod idemque tertium. Soph. 

. . Elench. 

vel in quo extrema conveniant, vel cui unum con- 4.1. 
veniat, alterum difFerat. 

4. Medium non distributum'^ est anceps. Esto^^aLPr. 

^ I. 24. 1. 

equivalent to argumentum is ttiVti?, which, however, as em- 
ployed by Aristotle, is a rhetorical, not a logical term, llie r-K'^ U k.»^ 
origin of Aldrich's blunder it is difficult to conjecture. ^j>. dy^Civ's { i,^*.^ /*> "' 

° Major premise ; rj irpos tw fxelCovi aKpto irporao-ts. Minor 
premise ; rj irpbs t(o eXdrrovi aKpco Trporao-is. Conclusion ; crvfiTre- 
paa-fia, which also signifies minor term, Anal. Pr. ii. 14. The 
premise is not, properly speaking, called 6pos by Aristotle. In J 
such expressions as KadoXov ovtcov twv opcov, (Anal. Pr. i. 5. 2.) I 
there is an ellipsis of npos t6v erepov, and the phrase means I 
strictly, that one term is predicated universally of the other, / 
i. e. of the whole of the other. 

p As by Cicero, de Invent, i. 37. Fortunatianus, Rhet. lib. ii. 
Cassiodorus, de Art. ac Disc. ch. 2. Boethius, de Syll. Hyp. 
p. 614. The terms are of Rhetorical origin. Quintilian calls 
the major premise, Intentio; Inst. Orat. v. 14. The conclusion 
is called complexio ; a term also applied by Cicero to the 
Dilemma ; de Inv. i. 29. 

** Distribution is not an Aristotelian term. It forms part of 



70 ARTIS LOGlCiE 

enim B terminus communis in b et /3 divisibilis ; 
Ergo h et 13 sunt opposita : et tamen vera dicitur 
Aliquod B. est b et Aliquod B est 13, Quare 
aliquod B est Medium anceps. 

5. Quare Medium in praemissis semel ad mini- 
mum distribui debet ; sufficit tamen, si vel semel 
distribuatur. Nam 1. ad probandum A est C, 
conveniat C alicui B, et A omni ; Ergo eidem 
alicui B : Ergo affertur unum aliquod idemque 
tertium &c. 2. ad probandum A non est C, 
conveniat C alicui B, et A differat omni ; Ergo 
eidem alicui B : Ergo affertur &;c. 

6. Processus ab extremo non distributo in 
praemissis, ad idem distributum in conclusione, 
vitiosus est. Nam ex aliquo non sequitur omne, 
Esto enim verum quod aliquod ; Ergo potest esse 
verum quod aliquod non ; (nam Subcontrariae 
possunt esse simul verae ;) Ergo de aliquo potest 
affirmari quod non de omni. Esto rursus verum 

what the Schoolmen call parva logicalia ; a kind of appendix 
to analyses of the Organon ; containing matters, some evolved 
from, though not distinctly treated of by Aristotle, others com- 
plete innovations, more properly belonging to Grammar than 
to Logic. The greater part of these first appear in Petrus 
Hispanus. See Summulce Logicales, Tr. 7. 

The syllogistic rules concerning distribution are of course 
implied in Aristotle's account of each figure, though not 
enunciated separately as common to all. Thus, to say that 
the major premise in fig. 1. must be universal, or one premise 
in fig. 2, negative, is equivalent to a rule for distributing the 
middle term. The particular conclusion in fig. 3. in like 
manner forbids an illicit process of the minor term. 



RUDIMENTA. 71 

quod aliquod non : Ergo potest esse verum quod 
aliquod : Ergo de aliquo potest negari quod non 
de omni. 

7. Prsemissis negantibus nihil probatur : Affer- Anal. Pr. 

I 24 1 

tur enim tertium cui utrumque extremum difFert ; * ' ' 
non autem cui vel utrumque conveniat, vel unum 
conveniat, alterum differat. 

8. Si praemissarum altera sit negativa, erit etiam 
Conclusio. Nam praemissarum reliqua est affirma- 
tiva : Ergo extremorum unum difFert medio, alte- 
rum convenit : Ergo extrema difFerunt inter se : 
Ergo conclusio est negativa. 

9. Contra, si Conclusio sit neerativa, erit etiam Anai. Pr. 

1 . XT TrY» . 1.24.4. 

altera praemissarum. Nam extrema diiierunt mter 
se : Ergo eorum unum convenit medio, alterum 
difFert : Ergo praemissarum altera affirmat, reliqua 
negat. 

10. Praemissis particularibus nihil probatur. Nam Anai. Pr. 
praemissarum altera affirmat : Ergo in ilia medium 

non distribuitur : Ergo distribui debet in reliqua : 
Ergo ilia est negativa in qua medium praedicatur : 
Ergo conclusio negativa : Ergo praedicatum ejus 
distribuitur, quod in praemissis non est distri- 
butum ; Fuit enim vel affirmativae terminus alter, 
vel subjectum negativae ; horum vero nuUus distri- 
buitur. 

11. Si praemissarum altera particularis sit, con-Auai. Pr. 
clusio quoque particularis est. Sit enim 1. Prae- 
missarum altera particularis affirmativa ; Ergo in 

ilia nee extremum suum nee medium distribuitur : 



72 ARTIS LOGlCiE 

Ergo medium distribuitur in reliqua, quae etiam 
Universalis est, sitque 1. Affirmativa : Ergo in ilia 
medium subjicitur, et extremum medio attributum 
non distribuitur : Ergo neutrum extremorum dis- 
tribuitur in praemissis : Ergo neutrum in con- 
clusione : Ergo conclusio particularis affirmativa 
est. Sit 2. Negativa : Ergo conclusio negativa : 
sed debet habere extremum non distributum : 
Ergo particularis negativa est. 

Sit 2. Pragmissarum altera particularis negativa : 
Ergo Reliqua Universalis affirmativa: Ergo in prae- 
missis duo tantum termini distribuuntur : Ergo 
Conclusio habet extremum non distributum : Ergo 
cum negativa sit, erit etiam particularis. 
An.Pr. I. 12. Quod si CoHclusio'' particularis sit, non 
necesse est praemissarum alteram particularem 
esse. Fieri enim potest, ut instituto meo sufficiat 
subalternata, quando subalternans potuit inferri. 
Et cum illae sint simul verae, liberum est utramvis 
inferre. Quanquam stricte loquendo, Argumentatio 
non est accurata ; nam Subalternatae Veritas non 
immediate deducitur ex praemissis, sed ex sub- 
altern ante. 



r This rule is given by Aristotle, not with reference to the 
subaltern moods, but to the third figure, in which two uni- 
versal premises only warrant a particular conclusion. An 
inverse rule of inference holds with regard to truth and 
falsehood : two true pi'emises necessitate a true conclusion ; 
but the truth of the conclusion does not guarantee that of 
the premises. Cf, An, Pr. ii. 2. 1. 



i 



RUDIMENTA. 73 

Syllogismi generales regulas complectitur hoc 
Tetrastichon^ 

Distribuas medium ; nee quartus terminus adsit. 
Utraque nee praemissa negans^ nee particularis. 
Sectetur partem Conclusio deteriorem. 
Et non distribuat, nisi cum praemissa, negetve. 

§. 4. SuPEREST per hasce regulas inquirere, quot 
modis componi possunt tres Propositiones de inesse, 
ut Syllogismum conficiant. Qua in inquisitione duo 
I spectanda sunt. 

1. Modus \ sive legitima determinatio Pro- 

^ The earliest form of this mnemonic is that given by 
Petrus Hispanus : 

Partibus ex puris sequitnr nil, sive negatis. 

Si qua prdeit partis, sequitur conclusio partis. 

Si qua negata praeit, conclusio sitque negata. 

Lex generalis erit, medium concludere nescit. 
* Mood (rpoTToy) is not in this sense an Aristotelian expres- 
sion, (unless possibly in An. Pr. i. 28. 14?) ; but it is found 
in his Greek commentators. See Alexander, Schol. p. 1 50, b. 3. 
Aristotle in the same sense employs tttoxtis, An. Pr. i. 26. 1. 
He does not adopt an arithmetical calculation of possible 
moods distinct from considerations of figure, but shews, in 
each figure separately, what combinations of propositions are 
admissible, and what not. It may be observed, that the 
earliest scholastic Logicians do not consider Mood as com- 
posed of three propositions, but of the two premises only. 
Thus Petrus Hispanus defines " ordinatio duarum proposi- 
tionum in debita qualitate et quantitate;" so Aquinas, in 
Opusc. xlviii. de Syll. ch. 4. In this case the number of 
possible moods is only sixteen. 

This computation is preferable to Aldrich's, because sim- 
pler; but neither has any logical value. The legitimate 



74 ARTIS LOGICS 

positionum secundum Quantitatem et Qualita- 
tem. 

2. Figura, sive legitima dispositio Medii cum 
partibus Qusestionis. 

Modi sunt in universum 64. Nam, ut supra 
ostensum est, ad Syllogismum faciunt Propositiones 
tantum quatuor A. E. I. O. Quare concipi potest 
Quadruplex tantum Major in Syllogismo ; cuilibet 
vero Majori quadruplex tantum Minor adjimgi; 
unde 16. paria praemissarum : et singulis praemissis 
quadruplex tantum Conclusio ; unde 64. Modi 
Syllogismorum. 

AAA. AAE. AAI. AAO. *AEA. AEE. AEI. 
AEO. *AIA. AIE. AIL AIO. *AOA. AOE. AOL 
AOO. 

EAA. EAE. EAL EAO. *EEA. EEE. EEL 
EEO. *EIA. EIE. EIL EIO. *EOA. EOE. EOL 
EOO. 

lAA. lAE. lAL lAO. *IEA. TEE. lEL lEO. 
*IIA. HE. in. 110. *IOA. lOE. lOI. 100. 

OAA. OAE. OAL OAO. *OEA. OEE. OEI. 
OEO. *OIA. OIE. OIL 010. *00A. OOE. OOL 
000. 

Ex his excluduntur sedecim per Regulam 7. 

determination ought to be such as the laws of Logic require ; 
not one which arises from a mere arithmetical calculation. 
^ On logical grounds, there are eight valid combinations of 
M premises; viz. AA. AE. AI. AO. EA. EI. lA. QA . The con- 
clusion, being determined by the premises, cannot properly 
be reckoned as an independent element in the combinations. 
Cf. Fries, System der Logik, §.57. 



RUDIMENTA. 75 

propter prsemissas negantes, viz. EEA. EEE. EEL 
EEO. *EOA. EOE. EOI. EOO. *OEA. OEE. 
OEI. OEO. *00A. OOE. 001. 000. Duodecim 
per Reg. 10. propter prsemissis particulares, viz. 
IIA. HE. III. 110. *IOA. lOE. lOI. 100. *OIA. 
OIE. OIL 010. Duodecim per Reg. 8. quia 
praemissarum altera negat, sed non Conclusio, viz. 
AEA. AEI. AOA. AOL *EAA. EAL EIA. EIL 
*IEA. lEL *OAA. OAI. Octo per Reg. 11. quia 
praemissarum altera particularis est, sed non Con- 
clusion viz. AIA. AIE. AOE. *EIE. *IAA. lAE. 
*IEE. *OAE. Denique quatuor per Reg. 9. quia 
Conclusio negativa est sed neutra praemissarum, 
viz. AAE. AAO. AIO. *IAO. 

Excluduntur igitur in universum Modi 52 = 16 
+ 12 + 12 + 8 + 4. e quibus multi contra plures 
regulas peccant, quamvis una tantum notetur. 

Supersunt (64 — 52 = ) 12 Modi ad Syllogismum 
utiles, viz. AAA. AAI. AEE. AEO. AIL AOO. 
*EAE. EAO. EIO. *IAL lEO^ *0A0. 

§. 5. FiGURiE'' Syllogismorum sunt 4. Nam 

" lEO has been condemned ever since the days of x'^puleius, /• ;^ ' 
as far as the second and third figures are concerned. It was 
sometimes allowed in the first, as the indirect mood Frisesmo, 
but should not have been retained by Aldrich, who does not 
recognise the indirect moods. With a direct conclusion, it ' 
manifestly produces an illicit process of the nmjor term4^j.,,,^v4-Y " 

^ FigurcB, a-xnixaTa, An. Pr. i. 4. 15. "Figuras syllogismoruffiT"^ 
quae dicuntur (Apuleius 'formulas' vocat), ab Aristotele ap- 
pellatas esse Jul. Pacius putat, quia figuris geometricis ad- 



76 ARTIS LOGICS 

Medium, quod cum utroque extreme comparatur, 
vel 1. subjicitur majori et tribuitur minori, et fit 

scriptis syllogismi ab eo illustrati sint. Equidem banc vocem 
non tam a geometricis petitam quam de ipso ordine termi- 
norum accipiendam putaverim, quern (rxvH-a appellari licebit, 
etiam si de geometricis figuris non cogitetur : sic enim supra 
commemoravimus ra crxwara ttjs Kanryopias (Metaph. V. 2. 1.), 
TO o'xVH'fi T^s- Ideas (Metapb. vi. 3. 2.), ra o-xVfJ-aTa tt]s Xe^ecoy 
(Poet. ]9. 7.), a-xvi^d TV drjfioKparias (Polit. vi. 4. 5.)." Waitz, 
vol. i. p. 384. On tbe otber band, Sir W. Hamilton, in a 
very interesting paper in tbe second edition of bis Discussions, 
p. 666. maintains tbe opinion of Pacius, and proposes a re- 
storation of tbe Aristotelian diagrams. Tbis dissertation 
contains a fund of valuable matter on tbe bistory and pbi- 
losopby of Logic, wbicb will well repay a careful perusal. 

Aristotle acknowledges only tbree figures ; looking ratber to 
tbe extension of tbe middle term, as compared with tbe otber 
two, tban to its position in tbe two premises. In tbis point 
of view tbere are only tbree figures possible ; for tbe relative 
extensions of tbe major and minor terms being given, the 
middle can only have tbree positions ; between tbe otber 
two, as in tbe first figure; greater tban both, as in tbe 
second ; or less tban both, as in tbe third. See Trendelen- 
burg, Elem. §. 28. Waitz on Anal. Pr. i. 23. 7. The invention 
of the fourth figure is attributed by Averroes (on Anal. Pr. 
i. 8.) to Galen. The latter may possibly have first called the 
five moods by that name, but they were known at a much 
earlier period as indirect moods of the first figure. An in- 
direct mood is one in which we do not infer tbe immediate 
conclusion, but its converse. Consequently, the predicate 
of the conclusion, which in a direct mood is the major term, 
is in an indirect one tbe minor. Tbe five indirect moods 
of the first figure were called Baralip, Celantes, Dabitis, 
Fapesmo, Frisesmo. The three first are clearly Barbara, 
Celarent, Darii, with the conclusions converted. With regard 
to the two last, tbe process is a little more intricate. They 
have negative minor premises, and thus offend against a 



RUDIMENTA. 77 

\jigura prima; vel 2. tribuitur utrique, et fit secunda; 
vel 3. subjicitur utrique, et fit tertia; vel 4. tribuitur 
majori et subjicitur minori, et fit quarto. Quae 
omnia sequenti Schemate declarantur. 

Dispositio trium terminorum, scilicet majoris 

A, medii B. minoris C in Figura, 

1. 2. 3. 4. 

B. A. A. B. B.A. A.B. 

C.B. C.B. B.C. B.C. 

C.A. C.A. C.A. C. A. 

Quare quselibet Figura excludit adhuc sex 

modos^ Nempe 



special rule of the first figure ; but this is checked by a 
counterbalancing transgression. For by simply converting 
0, we alter the distribution of the terms, so as to avoid an 
illicit process. T^ius, 



All B is A (fap) 

No C is B (esm) 

Therefore Some A is not C (o) 

Where to infer " Some C is 

not A," would involve an illicit 

process of the major term. 



Some B is A (fris) 

No C is B (esm) 

Therefore Some A is not C (o) 

Where to infer " Some C is 
not A," would involve an illicit 
process of the major term. 



The invention of these indirect moods is attributed to 
Theophrastus ; not, however, on the authority of Apuleius, as 
asserted by M. St. Hilaire, but on that of Alexander, Schol. 
p. 153, a. 47. But they were clearly recognised by Aristotle; 
the last two in Anaf. Pr. i. 7. 1. the first three in Anal. Pr. ii. 
1. 2. The passage in Apuleius does not refer to the indirect, 
but to the indefinite, syllogism. 

y Certain moods, not excluded by the general rules of 
syllogism, are rejected in some one figure, by what are called 



78 ARTIS LOGIC.E 

1. Propter Medium non distributum. Prima 
duos lAI. OAO. Secunda quatuor AAA. AAI. 
AIL lAI. Quarta duos AIL AOO. 

2. Propter processum majoris illicitum. Prima 
quatuor AEE. AEO. AOO. lEO. Secunda duos 
lEO. OAO. Tertia quatuor AEE. AEO. AOO. 
lEO. Quarta duos lEO. OAO. 

3. Propter processum minoris illicitum. Tertia 
duos AAA. EAE. Quarta duos AAA. EAE. 

Supersunt Modi certo et necessario concludentes 
24. sex in qualibet Figura. 

I. 

bkr Omne B est A 

bk Omne C est B : Ergo 

rk Omne C est A. 



the special rules of that figure. These special rules are given 
as follows by Petrus Hispanus. 

1 1. Minore existente negativa nihil sequitur. 
^^ * 12. Maj ore existente particulari nihil sequitur. 
1. Maj ore existente particulari nihil sequitur. 
Fig. 3. ■ 3. Ex puris affirmativis nihil sequitur. 

\3. In secunda figura semper concluditur negative. 
f 1. Minore existente negativa nihil sequitur. 
°* ' Is. In tertia figura conclusio debet esse particularis. 
These rules are all to be found in An. Pr. i. ch. 4, 5, 6. Of 
the fourth figure three special rules have been framed ; viz. 
1. '* Quando major est affirmativa, minor semper est uni- 
versalis." Q. " Quando minor est affirmativa, conclusio est 
semper particularis." 3. " In modis negativis, majorem 
universalem esse oportet." ^ 



RUDIMENTA. 79 

cE Nullum B est A 

/A Omne C est B : Ergo 

rEnt Nullum C est A. 

dA Omne B est A 

rl Aliquod C est B : Ergo 

I Aliquod C est A. 

/E Nullum B est A 

rl Aliquod C est B : Ergo 

Aliquod C non est A. 

A Omne B est A 

A Omne C est B : Ergo 

1 Aliquod C est A. 

E Nullum B est A 

A Omne C est B : Ergo 

O Aliquod C non est A. 



11. 

cEs Nullum A est B 

A Omne C est B : Ergo 

rE Nullum C est A. 

cAm Omne A est B 

Es Nullum C est B : Ergo 

trEs Nullum C est A. 



80 





ARTIS LOGIC.E 


/E. 


Nullum A est B 


^I 


Aliquod C est B : Ergo 


nO , 


Aliquod C non est A. 



bAr Omne A est B 

O^ Aliquod C non est B : Ergo 

O Aliquod C non est A. 

E Nullum A est B 

A Omne C est B : Ergo 

O Aliquod C non est A. 

A Omne A est B 

E Nullum C est B: Ergo 

O Aliquod C non est A. 



III. 

dAr Omne B est A 

A^ Omne B est C : Ergo 

tl Aliquod C est A. 

/E/ Nullum B est A 

Ap Omne B est C : Ergo 

tOn Aliquod C non est A. 

dls Aliquod B est A 

Am Omne B est C : Ergo 

Is Aliquod C est A. 



I 



RUDIMENTA. 



81 



bOk Aliquod B non est A 

Ar Omne B est C : Ergo 

dO Aliquod C non est A. 

d\t Omne B est A 

Is Aliquod B est C : Erga 

I Aliquod C est A. 

fEr Nullum B est A 

Is Aliquod B est C : Ergx> 

On Aliquod C non est A. 



IV. 

brAm Omne A est B 

An Omne B est C : Ergo 

tip Aliquod C est A. 



cAm 


Omne A 


est 


B 


Ew 


Nullum B 


est 


C: Ergo 


E5 


Nullum C 


est 


A. 



d\m Aliquod A est B 
Ar Omne B est C : Ergo 
\s Aliquod C est A. 



/E5 Nullum A est B 
Ap Omne B est C : Ergo 
O Aliquod C non est A. 

G 



82 ARTIS LOG1C.E 

frEs Nullum A est B 

Is Aliquod B est C : Ergo 
On Aliquod C non est A. 

A Omne A est B 

E Nullum B est C: Ergo 

O Aliquod C non est A. 

Barbara ^ Celarent, Darii, Ferioque, prioris : 
Cesare, Camestres, Festino, Bar oka, secundae : « 
Tertia, Darapti, Disamis, Datisi, Felapton, 
Bokardo, Ferison, habet : Quarta insuper addit 
Bramantip, Camenes, Dimaris, Fesapo, Fresison : 

^ Barbara, Celarent, &c. This mnemonic first appears in 
the SummuliB Logicales of Petrus Hispanus, (see on p. 48.) 
But in his version the fourth figure is omitted, and its moods 
given as indirect moods of fig. 1 . This earliest edition of these 
celebrated lines runs thus : 

Barbara, Celarent, Darii, Ferio, Baralipet, 
Celantes, Dabitis, Fapesmo, Frisesmo, deinde 
Cesare, Camestres, Festino, Baroco, Darapti, 
Felapton, Disamis, Datisi, Bocardo, Ferison. 
Several other versions are found in later writers. A Greek 
mnemonic of the same kind is inserted in editions of the 
Organon preceding that of Pacius. (See Buhle's Aristotle, 
vol. ii. p. 628.) It runs thus : 

Fig. 1. ypdjiixaTa — eypayj/e — ypacpldi — rexyiKos. 

Fig. 2. eypay^e — Kare;(e — perpicv — a)(o\ov. 

Fig. 3. anaa-L — adevapos — laaKis — (fiepto-ros — aa-TnSi — ofxakos. 
This mnemonic is attributed by M. St. Hilaire to Nicephorus 
Blemmidas ; but Sir W. Hamilton, in a note appended to the 
second edition of his Discussions, p. 669, has shewn that the 
Greek mnemonic is in all probability only an imperfect attempt 
at conversion into Greek of the Latin memorial of Hispanus. 



RUDIMENTA. 83 

Quinque Suhalterni, totidem Generalibus orti, 
Nomen habent nullum, nee, si bene colligis, usum. 

§. 6. Atque omnes quidem 24. eatenus con- 
cludere, quod *in iis convenientia vel dissidium 
extremorum certo atque necessavio colligatur, ex 
Principio primo et secundo abunde constat. 

Quod aliter demonstrat Aristoteles ad hunc 
modum. 

Statuit primo Theorema, quod Scholastici vocant Anai.Pr.i. 
Dictum de Omni et Nullo'', scil. " Quod praedicatur 

* Aeyofiev be to Kara navros narqyopelaOaL, orav fXTjdev rj Xa^clv tS>p 
rov vTTOKei^evov, KaG" ov Bdrepov ov Xex^rjcreTar kol to kuto firjbevos 
coaavTcos, An. Pr. i. 1. 8. The same principle is implied in 
the first antipredicamental rule, Categ. 3. 1. oo-a KaTo. rov kott]- 

yopovfievov Xeyerai ivdvTa Kol KaTO. tov VTroKCifievov pr]6f)aeTai. Indeed, 

Aldrich's version is more nearly a translation of the latter 
than of the Dictum properly so called. Cf. Petr. Hisp. Tract, iv. 
*' Dici de omni est, quando nihil est sumere sub subjecto, de 
quo non dicatur prsedicatum, Dici de nullo est, quando nihil 
est sumere sub subjecto a quo non removeatur praedicatum." 

The Dictum de Omni et Nullo is most improperly called a 
Theorem. This term in Aristotle is synonymous with Cn'^H-^y 
and means a proposition, the truth of which is to be inquired 
into, not one laid down as an axiom. See Topics, i. 11. 1. 
Alexander, Scholia, p. 259, a. 38. 

The dictum is directly applicable only to the first figure, 
which- is considered by Aristotle as the type of all syllogisms, 
and to which the others have to be reduced, as a necessary 
test of their validity. In this he is followed by Kant, Logik, 
§. 69. Other Logicians enunciate distinct axioms for the 
second and third figures. This has been done by Lambert, 
Neues Organon, part i. ch. 4 §. 232. but he is far from happy 
in his enunciation of the dicta. We may state them as follows, 
in a somewhat improved form. 

g2 



84 



ARTIS LOGICi*: 



" Universaliter de alio, (i. e. de termino distribute,) 
'' sive affirmative, sive negative, praedicatur similiter 
" de omnibus sub eo contentis." 

Principle of second figure. Dictum de Diverso. 

If a certain attribute can be predicated (affirmatively or 
negatively) of every member of a class, any subject, of which 
it cannot be so predicated, does not belong to the class. 

Principles of third figure. I. Dictum de Exemplo. 

If a certain attribute can be affirmed of any portion of the 
members of a class, it is not incompatible with the distinctive 
attributes of that class. 

II. Dictum de Exeepto. If a certain attribute can be denied 
of any portion of the members of a class, it is not inseparable 
from the distinctive attributes of that class. 

The natural use of the second figure, according to Lambert, 
is for the discovery and proof of the differences of things : that 
of the third, for the discovery and proof of examples and 
exceptions. 

Concerning Lambert's imaginary principle of the fourth 
figure, see p. 9 1 , note n. Lambert's principles are criticised 
by Krug, Logik, §. 109. According to Sir W. Hamilton, 
{Discussions, 2^d Ed. p. 666.) " it was Melanchthon who first 
excogitated, as he thought, the various principles on which 
proceed the various syllogistic figures." The following may 
be gathered from his Erotemata Dialectices. 

Principle of first figure, Posito genere, necesse est speciem 
poni. 

Principle of second figure. Remoto genere, removetur species. 

Principle of third figure. Posita specie, necesse est genus 
poni, sed particulariter. 

There is a third manner of treating the syllogistic figures ; 
viz. by regarding them as all equally direct applications of 
one and the same principle. This has been attempted by 
Aldrich and others in the Canons ; (see p. 66.) but inaccm-ately. 
The three ultimate Laws of Thought are the Principles of 
Identity, of Contradiction, and of Excluded Middle. These 
ai'e directly applicable to all the syllogistic figures alike. 



RUDIMENTA. 85 

Admisso hoc Theoremate (quod axioma sponte 
perspicuum est) constat una, modos quatuor 
priores in prima certo atque necessario concludere. 
Nam eorum major ostendit majus extremum prse- 
dicari de medio distributo ; et minor, minus ex- 
tremum sub medio contineri. 

Quare, Modi quatuor praedicti nihilo penitus 
indigent quo necessitas conclusionis appareat, 
praeter ea quae in praemissis posita sunt ; et proinde 
quatuor illi sunt prae caeteris evidentes. Nam 
caeteri omnes aiiquo vel aliquibus egent, quae, 
utcunque per praemissas necessaria, in Syllogismo 
tamen non exprimuntur. Quare illos Aristoteles Anai.Pr.i. 
perf ectos^, \io^ imperf ect OS di\c\t\ SchoXdi^Wci direct os. 

Other general principles, but less accurate, have been given 
by the Port-Eoyal Logic, part iii. ch. 10. by Buffier, Principes 
du Haisonnement, Let. vi. vii. and by Euler, Lettres a uns Prin- 
cesse d'Allcmagne, p. ii. 1. 36. ed. Cournot. For a criticism of 
the Port-Royal principle, cf. Duval-Jouve, Logique, p. 306. 

^ TeXeiov (xeu ovv koKo) (TvXkoyicrfibv tuv firjdevos aXXov npoadeo^evov 
irapa to. etXrjfxixeva Trpos to (PavTJvai to dvayKoiov, dTeXrj 6e top npocr- 
beopevov fj evos y nX^ioucov, a eaTi, pev avayKoia dia tcov vnoKeipeuoiv 
opcBf, ov prjv (iXrjTTTai Sta TrpoTaaecov, Anal. Pr. i. 1. 7. With 

Aristotle, the " dictum de omni et nuUo" is the principle of 
all syllogism ; and the conversions, &c. required by the im- 
perfect syllogisms, must be performed before their conclusions 
are admitted as valid. 

The direct and indirect syllogisms of the Schoolmen must 
not be confounded with the perfect and imperfect of Aristotle. 
An indirect syllogism is one in which the minor term is the 
predicate, the major the subject of the conclusion. See Aquinas, 
Opusc. xlviii. de Syll. cap. 8. Scotus, super lib. I. Anal. Prior, 
QusBst. xxii. sqq. Occam, Logica, p. iii. cap. 6. Of these in- 
direct moods, five were admitted in the first figure, two in 



7.3 



86 ARTIS LOGICS 

et mdirectos vocant : quia per illos ad conclusio/nem, 
velut ad scopum, recta itur ; per reliquos eodem 
perveniri potest, prius tamen alio deflectendum est. 
An. Pr. I. Perfici" igitur et revocari at que reduci dicimus 
1. 23. i. indirectos, cum per modum aliquem directum 
illationis suae vim demonstrant. Et definitur 
Reductio^, imperfecti Modi in perfectum mutatio, 
quo necessitas illationis fiat ex inevidenti evidens. 
Fiet autem, quando evidenter (h. e. in prima) 
ostenditur conclusionem vi prasmissarum vel 1. 
An. Pr. I. talem esse ; vel 2. aliam esse non posse. Unde 
Reductio est vel osteiisiva vel ad impossihile^, 

the second, (by converting the conclusions of Cesare and 
Camestres,) three in the third, (by converting the conclusions 
of Darapti, Disamis, and Datisi.) Cf. Anal. Pr. i. 7. ii. 1. Of 
these, the five in the first figure are the most important, being 
sometimes regarded as a fourth figure. See p. 75, note x. 
The perfect and imperfect moods of Aristotle are sometimes 
called immediate and ynediate. Cf. Aquinas, Op. xlviii. cap. 1. 
Occam, Log. p. iii. cap. 2. Boethius calls them indem^onstrahle 
and demonstrable. 

^ Perjici, — TeXeiovadai, iiiLTeKetaOai; {jekelaxris OCCUrs An. Pr. i. 
25. 8.) Reduci, dvdyeaOat, (never dndyeo-Oai:) oste)isively, deiKTiKws. 

^ Reductio. The value of Keduction in Logic will depend 
: on the principle adopted as the basis of the syllogism. In 
the systems of Aristotle and Kant, whose principles ai-e im- 
mediately applicable only to the first figure, reduction is 
necessary. In the system of Lambert, in which each figure 
rests on a separate axiom, reduction is impossible ; the 
process being then the destruction of one distinct reasoning, 
and the substitution of another. By reducing the laws of 
thought to their simplest form, in which they are applicable 
to all syllogisms directly, reduction is superfluous. 

« Reductio ad impossihile. This phrase, though sanQtioned 



RUDIMENTA. 87 

Utriusque praxin pro Modis nominatis decent 
ipsa Modorum nomina a Scholasticis in hiinc 
finem conficta. Nam in iis tres vocales sunt 
totidem propositiones Syllogismi sua quantitate et 
qualitate signatae. Consonae initiales B. C. D. F. 
notant modum primae, ad quem sit Reductio. 
S. P. propositionem, quam vocalis proxime ante- 
cedens designate esse in Reductione convertendam : 
S simpliciter ; P per accidens. M transponendas 
esse praemissas. K reductionem fieri per impos- 
sible, i. e. pro praemissa, cujus symbolo adhaeret^ 
sumendam esse Conclusionis contradictoriam *. 
Quibus ex praescripto factis, colligitur in prima 

by respectable authorities, is incorrect; as may be shewn by 
substituting the definition. What is the meaning of " the 
change of an imperfect to a perfect mood to the impossible?" 
The error has been caused by the Aristotelian expression, 
airayoiyri els to advvarov ; in which, however, diraycdy^ does not 
mean reduction. The deductio ad impossihile, as it is usually 
rendered, {ahductio would perhaps be better,) is one species 
of the (Tv\Xoyi(Tfi6s e$ vTTodeo-eas, (see Appendix, note I,) the 
object of which is, to prove the truth of a given problem, by 
inferring a falsehood from the assumption of its conti'adictory. 
This may be emplo^^ed in the reduction of syllogisms, but it 
is also used for other purposes, as by Geometers. (Euclid, i. 7.) 
The correct expression is therefore Reductio per deductionem ad 
impossibile, or elliptically, Redtictio per imp>ossihile. The aTraywyiy 
of An. Pr. ii. 25. will be explained hereafter. 

Any mood may be reduced by the deductio ad impossibile, 
though in practice it is usually confined to Baroko and 
Bokardo. 

*■ Whence the lines, 

S vult simpliciter verti ; P vero per acci : 

M vult transponi ; C [Kj per impossibile duci. 



88 ARTIS LOGICiE 

conclusio vel expositas eadem, vel earn inferens, 
vel prasmissse contradictoria^ ut in exemplo. 



cEs 


Nullum 


A 


est 


B 




Ar 


Omne 


C 


est 


B: 


Ergo 


E 


Nullum 


C 


est 
ad 


A. 




cE 


Nullum 


B 


est 


A 




Ik 


Omne 


C 


est 


B: 


Ergo 


rEnt 


Nullum 


C 


est 


A. 




dls 


Aliquod 


B 


est 


A 




Am 


Omne 


B 


est 


C: 


Ergo 


Is 


Aliquod 


C 


est 
ad 


A. 




dk 


Omne 


B 


est 


C 




rl 


Aliquod 


A 


est 


B: 


Ergo 


I 


Aliquod 


A 


est 


C. 




hkr 


Omne 


A 


est 


B 




Ok 


Aliquod 


C 


non est 


B: 


Ergo 





Aliquod 


C 


non est 
ad 


A. 




bkr 


Omne 


A 


est 


B 




hk 


Omne 


C 


est 


A: 


Ergo 


rk 


Omne 


C 


est 


B/ 





g Archbishop Whately gives an ostensive reduction of 
Baroko and Bokardo to Ferio and Darii, by converting the 
major premise by contraposition. Logic, b. ii. c. 3r~^§. 5. 



RUDIMENTA. 89 

§. 7. Reductionis ostensivse validitas sic osten- 
ditur. Ex praemissis reducendi, per conversionem 
imperatam^ necessario colliguntur praemissse re- 
ducti : atque ex iis^ per figuram primam, conclusio 
reducti : quae vel ipsa conclusio reducendi erit^ vel 
per illativam conversionem fiet. 

Reductionis per Impossibile validitas sic osten- 

ditur. Quoniam praemissae ex hypothesi sunt 

I semper verae, ergo contradictoria praemissse nun- 

j quam vera : ergo contradictoria conclusionis nun- 

I quam vera : (nam has simul veras esse demon- 

stratur in Barbara) ergo contradictoria conclusionis * 

semper falsa : ergo conclusio ipsa semper vera, 

[Reducitur etiam quilibet modus innominis, 
facto quod praecipitur, ad prsemissas sui subalter- 
nantis. Tum vero conclusio, quae colligitur in 
prima, erit vel expositae subalternans, vel in expo- 
sitam per accidens convertetur. 

Reductiones' (cum primae ad reliquas, tumAn.Pr. i. 

45.1. 

This had been done before ; partly by Jung, in the Logica 
Hamburg ensis, B. III. ch. 12. §. 15. and partly by Wolf, Philo- 
sophia Rationalis, §.384. 

^ Since a false conclusion cannot be drawn without at least 
one false premise, see An. Pr. ii. 2. 1. But in the present 
syllogism, one premise is given true, being one of those of the 
original syllogism ; the other, therefore, is false, which is the 
contradictory of the original conclusion. The syllogism ad 
impossibile will not always be in Barbara ; though it is so in 
the reduction of Baroko and Bokardo. 

^ Of these reductions, it need only be observed, that they 
are only possible where the same problem can be proved in 
both figures ; hence only negative syllogisms can be reduced 



90 ARTIS LOGICS 

earum ad se invicem) bene multas, quod et obviae 
sint^ et institute nieo minus necessarise, praeter- 
An. Pr. 1. mitto. Illud tamen notatu dignum est, quod 
cum Darii ad Camestres, et Ferio ad Cesare redu- 
catur per impossibile, uterque igitur ad Celarent ; 
omnisque adeo modus reducitur ad duos universales 
primae.] 

§. 8. Perspicuum est ex antedictis 

1. Syllogismos simplices, certo atque necessario 

concludentes, fieri 24 modis : 6 in qualibet figura. 

An. Pr. i! 11. Et in aliquo istorum modorum probari posse 

conclusionem quamlibet de inesse ; nempe A uno 

modo, E quatuor, I septem, O duodecim\ Et 

An. Pr. I. rursus ; in prima, conclusionem quamcunque : In 

An. Pr. I. secunda, omnes et solas ne2:ativas : In tertia, omnes 

5. ]6. o " 

An. Pr. I. et solas particulares : In quarta, quamlibet praeter 
A. De praemissis denique, quod in prima et 
secunda, major semper universalis est ; in prima et 



to the second figure, and only particular syllogisms to the 
third. Barbara, Baroko, and Bokardo, cannot be ostensively 
reduced to any other figure, except by the use of conversion by 
contraposition. 

^ Kejecting the fourth figure and the subaltern moods, it 
will be better to say with Aristotle ; A is proved only in one 
figure and one mood, E in two figures and three moods, I in 
two figures and four moods, O in three figures and six moods. 
For this reason, A is declared by Aristotle to be the most 
difficult proposition to establish, and the easiest to overthrow; 
O, the reverse. And, generally, universals ai'e most easily 
overthrown, particulars more easily established. ^ 



RUDIMENTA. 91 

tertia, minor affirmativa: In secunda, praemissarum 
altera negativa : aliaque ejusmodi ; quae ipsa 
modorum nomina satis indicant ^ 

At que hinc facile colligitur, inspecto schemate An, Pr. i. 
modorum^ quali medio probanda sit quaestio omnis i. 32. 10. 
de inesse. e. g. Quaestio A probatur in Barbara ; 
medio, de quo praedicatum quaestionis universaliter 
affirmatur, quodque de subjecto quaestionis affir- 
matur itidem universaliter : et sic de caeteris. 

Adverte tamen quod imperite disputantis est 
afFerre modum innominem ; ponet enim in prae- 
missis plusquam opus est ad conclusionem. Quare 
et innomines hactenus sunt incensi ; quamvis 
negari nequeant, sicubi per inscitiam adhibentur"". 
,. Adverte etiam, quod figura quarta tribus 
caeteris deterior est ; cum aliis de causis, tum ex 
hoc praesertim, quod medium dicat de majori, 
huric de minori, minorem de medio, h. e. medium 
nugatorie de seipso". 

^ See p. 77, note y. 

"• The invention of the five anonymous moods is attributed 
by Apuleius to Aristo of Alexandria. 

" This objection is brought against Galen by Averroes, on 
Anal. Post. I. 8. It might be better stated, majorem nugatorie 
de seipso. Reckoning backwards from the conclusion, we find 
that the major contains the minor, the minor the middle, the 
middle the major; so that, in fact, the major contains itself. 

The fourth figure has been defended by Lambert, who 
declares it to be useful for the discovery or exclusion of the 
species of a genus. He frames a principle for it, called dictum 
de reciproco. I. If no M is B, no B is this or that M (Ca- 
menes). II. If C is or is not this or that B, there are B's 



92 ARTIS LOGICS 

III. Syllogismis etiam adnumerantur aliae argu- 
mentorum species ; quae nee stricte loquendo 
Syllogismi sunt, nee ita tamen peccant, ut prop- 
terea mereantur excludi : in quibus scilicet reticetur 
argumenti pars aliqua, sed quam proclive est cogi- 
tatione substituere. 
Anal. Pr. 1. Enthymema ; cuius antecedens constat pro- 

II 27 2 

Riet.i.*2. positione et judicio ; nam judicium est propositio 
in mente ° ; e. g. Homo est animal ; ergo est vivens. 

which are or are not C. (Bramantip, Dimaris, Fesapo, Fresison.) 
The principle is sufficiently clumsy ; the utility questionable. 
For the syllogism is not an instrument of discovery ; and how- 
can we prove the species of a genus by a particular conclusion? 
•* Some B is C," only proves a separable accident. It may be 
observed also, that the objection which Lambert urges, and 
with reason, against the conversion of the second and third 
figures, viz. that by conversion we often substitute an un- 
natural and indirect for a natural and direct predication, does 
not hold as regards the fourth. For, in the first three moods 
no conversion of premises is needed. By regarding the first 
stated as the minor, the second as the major, we obtain a 
much more natural conclusion in the first figure. Fesapo 
and Fresison establish exceptions, and therefore, on Lambert's 
theory, should more naturally fall into the third figure. The 
whole distinction, however, between natural and unnatural 
predication relates to the matter, not to the form of the 
thought. 

o Propositio in ynente. Aldrich had in his mind the absm'd 
etymology from iv dvtxc?, or as Versorius gives it, " ab en quod 
est in, thymos, quod est mens, et monos, quod est unum, quasi 
in mente retinens unam propositionem." The erroneousness 
of this etymology (besides its intrinsic absurdity) appears 
from the word hOvfirjixa being found in the Greek language 
before it assumed a technical meaning; e. g. Soph. CE. C. 292, 
1199. Some Logicians attempt to distinguish between the 



RUDIMENTA. 93 

Dicitur etiam Aristoteli Si/llogismus Oratorius ; et, 
si Integra ejus vis contineatur in unica propositione, 
senientia Enthifmematica ; utrumque Quintiliano Rhet. ii. 

, ,, ,. . . 21.6. 

sententia cum ratione ; ut, Mortalis cum sis, immor- 
tale ne geras odium. Deest illi ad Syllogismum 
altera praemissarum ; utrum vero major an minor, 
ex quaestione dignoscitur. 

2. Inductio ; in qua ponitur quantum opus est Anai. Pr. 
de singulis, et deinde assumitur de universis ; ut, 

Hic et ille et iste magnes trahit ferrum ; ergo omnis. 
Est igitur Enthymema quoddam ; nempe Syllo- 
gismus in Barbara p, cujus minor reticetur. 

3. Ejcem^lum ; (Aristoteli Inductio Oratoria'^) knsi.vr. 

Rhet. I. 

2 19 
Logical and the Rhetorical Enthymeme, (see Sanderson, b. iii. 

eh. 8.) The distinction is not authorized by Aristotle, and is 
liable to the objection which must always lie against a wanton 
alteration of the meaning of technical terms. For the Enthy- 
meme of Aristotle, see Appendix, note F. 

p The supposed minor is, of course, " All magnets are this, 
that, and the other." In this perversion, Aldrich has been 
preceded by Zarabella, De Meth. lib. iii. cap. 3. Archbishop 
Whately departs still further from Aristotle, and makes 
Induction a Syllogism in Barbara with the major premise 
suppressed. Thus : 

" That which belongs to this, that, and the other magnets, 
belongs to all ; 

Attracting iron belongs to this, that, and the other ; 

Therefore it belongs to all." ^ 

For the real nature of Logical Induction, see Appendix, 
note G. 

*> Aldrich considers the Example as an Induction ; i. e. 
according to his view, as a Syllogism in Barbara with the 
minor premise suppressed. The supposed minor, according 



94 ARTIS LOGICiE 

iibi quod ponitur de singular! noto, assumitur de 
simili ignoto : ut, Sylla et Marius Inceravere rem- 
publicam ; ergo Ccesar et Pompeius lacerahunt. 
Hujus etiam minor reticetur ; quapropter (ut in 
caeteris) quaestionem assumi dico ; neque enim 
colligitur nisi ex posito et subintellecto. 

4. Sorites^ ; in cujus Antecedente^ ex ordinata 

to this view, will be, " Csesar and Pompey are Sylla and 
Marius." But the example proper is not a logical reasoning 
at all; being a compound of an imperfect, and therefore 
illogical, Induction and a Syllogism. See further, Appendix, 
note H. 

' The Sorites is a series of propositions, in which the pre- 
dicate of each is the subject of the next; the conclusion being 
formed of the first subject and the last predicate. It may be 
expanded into a series of syllogisms in the first figure, the 
conclusion of each being the minor premise of the next. 
There will be as many syllogisms as there are intermediate 
propositions between the first premise and the conclusion; 
the first being the only minor premise stated. Hence there 
can only be one particular premise in a Sorites, the first ; the 
others being major premises in the first figure. And the last 
is the only premise which may be negative : for any previous 
negative premise would produce a negative conclusion, which 
could not be used as a minor premise in the next syllogism. 

The Sorites is not recognised as a distinct kind of reason- 
ing by Aristotle. Nor is there any reason why it should have 
been ; as it is merely a combination of ordinary syllogisms, 
succinctly expressed. Its distinct exposition is attributed to 
the Stoics. But the principle, as Melanchthon observes, is 
implied in Categ. 3, 1. and the Sorites itself is alluded to in 
Anal. Pr. i. 25. 2, 11. There is another form of the Sorites, 
called the regressive or Goclenian, first given by Goclenius in 
his Isagoge in Organum Aristotelis. In this, the subject of each 
proposition is the predicate of the next ; the conclusion being 



RUDIMENTA. 95 

serie terminorum, prsecedens quisque subjicitur 
sequent!, donee a subjecto qusestionis pervenitur 
ad prsedicatum, v. g. Homo est anhnal : animal est 
vivens : vivens est substantia ; ergo Homo est sub- 
stantia. In Sorite igitur subaudiuntur Syllogism! 
quot sunt intermediae propositiones ; (vel si mavis, 
quot in antecedente termini intermedii ;) unde et a 
curaulo nomen habet. 

5. Soriti affinis est Syllogismus, cujus prsemis- 
sarum altera est sententia Enthymematica^; ut, 
Nullus injustus est amandus : Omnis Tyrannus 
{crudelis cum sit) est injustus; ergo Nullus Ty- 
rannus est amandus. Qui quidem Syllogismus pe- 
culiare nomen non habet*; praemissae autem En- 
formed of the last subject and the first predicate. E. g. All 
D is E, all C is D, all B is C, all A is B ; therefore all A is E. 
In this, when expanded, the conclusion of each syllogism is 
the major premise of the next. In this Sorites, only the first 
premise can be negative and the last particular. This, as 
Krug has remarked, should really be called the progressive; 
the ordinary Sorites the regressive. A much more complicated 
theory of Sorites is given by Herbart, Lehrbuch zur Philosophies 
§. 70. and by Drobisch, Logik, §• 81 ; but it is of little logical 
value. 

The Sorites must not be confounded with the well-known 
fallacy of the same name, attributed to Eubulides of Miletus, 
and mentioned by Cicero, De Divinatione, ii. 11, In fact, the 
name has been loosely applied to various kinds of reasoning. 

' On the Enthymematic sentence, see Arist. Khet. ii. 21. 6. 

' It is sometimes called an epicheirema. The word originally 
was synonymous with Dialectic Syllogism. See Top. viii. 11, 
12. Of this epicheirema or argumentatio, the Khetoricians 
enumerated various kinds, tripartita, quadripartita, quinque- 
partita, dc. See ad Heren. ii. 2. ii. 19. Cic. de Inv. i. 37 sqq. 



1.39. 



96 ARTIS LOGICtE 

Anal. Pr. thymematicse antecedens, Aristoteli Prosyllogismus 

I. kjj. 11. ^^ 
1.28.5. est\ 

6. Hue denique revocandum est compendium 
illud disputandi opponentibus usitatissimum, reti- 
cendi scilicet conclusionem ; cum sit ipsa quaestio, 
quam respondens non supponitur ignorare. 

[Admittuntur denique in Scholis etiam Syllo- 
gismorum formulae, quia contra regulas voce 
tantum, non sensu, peccant, et mutata phrasi ad 
canonicas facile revocantur. Suntque nihil aliud 
quam licentise qusedam Syllogisticse, et in accurata 
disputatione non videntur admittendse. 
Anai.Pr. 1. Quaudo pro termino repetendo substituitur 
vox illi aequipollens. Ut in hoc. Ens naturale 
constans corpore organico et anima raiionali est 
homo: Socrates est ejiismodi : ergo est homo, et 
similibus. Potest enim Sophista abuti ista libertate 
vel ad nugandum vel ad fallendum. 

2. Quando fiunt Syllogismi ex obliquis, qualis 
est, Omnis hominis equus currit : Socrates est homo ;. 
ergo Socratis equus currit. Pro minori rectius 
dixeris Socratis equus est hominis equus, alias con- 
Quint. Inst. V. 13. Finally, the name Epicheirema was 
limited to the quadripartite. Cf. Trendelenburg, Elem. §. 33. 
Schweighfeuser on Epictetus I. 8. For some other variations 
in the use of the name, see Krug, Logik, §. 113. 

" Not exactly. The prosyllogism, or antecedent syllogism, 
of Aristotle, is a syllogism employed to prove one of the 
premises of another syllogism. It need not be expressed in 
a curtailed form. See Pacius on Anal. Prior, i. 35 3. Biese, 
vol. i. p. 157. 



I 



RUDIMENTA. 97 

sequentia, licet bona, non erit immediata. Atque 
|illo insuper laborat disputatio omnis ex obliquis, 
I quod praster necessitatem aperit locum fallaciae, 

3. Quando propositio aliqua intelligitur contra 
quam sonat, e. g. Quod non liahet partes non 
\intent per dissolutionem partkim : Aniyna liumana 
non liahet 'partes: ergo anima humana non interit 
per dissolutionem partium. Nam major sonat nega- 
tive, intelligitur vero affirmate : puta^ Quod interit 
&c. habet partes. Vel etiam singula propositiones 
intelliguntur affirmate, ac si esset Syllogism us, 
Omne expers est incorruptibile : Anima humana est 
expers ; ergo anima humana est incorruptihilis. 

Eodem accenseri possunt Syllogismi quales 
I Author Artis cogitandi^ vocat Complexos, in quibus 
etiam dijudicandis jactat se satis imperite. v. g. 
p. 164. laudat hunc Syllogismum, Lex divina jubet 
Reges honor ari: Ludovicus XIV est Rex; ergo 
Lex divina jubet Ludovicum XIV honor ari. Ubi 
valet certe Argumentum ; Syllogismus tamen est 



" Author Artis Cogitandi. The work alluded to is "I'Art 
de penser," commonly called the Port-Royal Logic. This 
work has been ascribed to various authors, but Avas most 
probably written by Arnauld, assisted by Nicole ; the first 
j edition was published at Paris in 1662. Aldrich has on more 
jthan one occasion spoken too slightingly of this very valuable 
iwork, the Logic par excellence of the Cartesian Philosophy. 
I For a better estimate of its merits, the reader is referred to 
I Stewart's Preliminary Dissertation to the Encyclopaedia Bri- 
tannica, p. 80. and to the Introduction to the recent able 
Translation of the Port-Eoyal Logic, by Mr. Baynes. 

H 



98 ARTIS LOGICtE 

falsissimus, cum habeat quinque terminos. Nam 
ex conclusione patet quod major terminus est 
juhet Ludovicmn XlVhonorari, et minor Lex divina: 
ergo minor Propositio Lex divina jubet Reges 
honor ari: ergo Medius terminus ^'2/6^^ Reges hono- 
rari : ergo Major Propositio debuit esse, Quoa 
jubet Reges honor ari, jubet Ludomcum XIV hono- 
rari ; et turn valeret Syllogismus ; nee redun- 
darent duo termini, qui in secunda propositione 
jam redundant. 

P. 166. Syllogismum hunc improbat^ Debemus 
credere Scripturce: Traditio non est Scriptura; ergo 
non debemus credere Traditioni ; quia eum scil. 
imperite reducit ad primam, cum tamen Syllo- 
gismus apertissime hoc dicat in secunda, Objectum 
jidei divince est Scriptura: Traditio non est Scrip- 
tura ; ergo Traditio non est Objectum Jidei divi?ice. 

Ibidem imperite autumat Syllogismum sequen- 
tem, in quo omnes propositiones videntur affir- 
mativae, esse in secunda ; salvari vero, quia minor 
sensu exclusiva, negativam in se contineat. Quod 
si ipsos Syllogismi terminos rite dignoscere potu- 
isset, vidisset sane Syllogismum esse in Barbara 
transpositis praemissis, v. g. Bonus Pastor estparatus 
animam ponere pro ovibus ; Pauci hoc smculo sunt 

"^ Syllogismum hunc improbat. In this instance, it is scarcely 
necessary to observe that the Port-Royal Logicians are right, 
and Aldrich is wrong. The premise does not state that 
nothing but Scripture is to be believed ; and therefore the con- 
clusion drawn is illogical. 



RUDIMENTA. 99 

parati &c. ergo Pauci hoc sceculo sunt Bo?ii Pas- 
tores. Hujus conclusio perspicue dicit (non de 
paucis, quod sunt Boni Pastores, sed) de Bonis 
Pastoribus, quod sunt hoc saeculo pauci. Quare 
Major terminus est hoc sceculo pauci, et Minor 
Boni Pastores. Ergo Minor Propositio, Boni 
Pastores sunt parati &c. et Medius terminus, 
parati animam ponere pro ovihis, Syllogismus vero 
hie est. Qui parati sunt animam ponere pro ovihus 
sunt hoc sceculo pauci : Qui sunt Boni Pastores sunt 
parati animam ponere pro ovibus : ergo qui sunt 
Boni Pastores sunt hoc sceculo pauci^. 

Haec dixisse erat operae pretium, nequis temere 
repudiaret eos qui, si non videntur, sunt tamen 
revera Syllogism!.] 

y Hoc sceculo pauci. Aldrich's solution is untenable. "Few" 
is not predicated distributively, but collectively. From " wise 
men are few," we cannot infer, •' Socrates is few." The 
syllogism, therefore, as stated by Aldrich, becomes a fallacy of 
division ; though, when tested by common sense, it is un- 
questionably valid. The Port-Royal Logicians substitute for 
the minor premise, Multi Pastores hoc scecuIo non sunt parati, 
dc. which is perhaps the most satisfactory way of treating the 
proposition, regarded as a single statement. But in fact it 
contains two distinct assertions; 1st, that some men are 
prepared ; 2dly, that most men are not. The reasoning 
should thus be resolved into two distinct syllogisms. See 
Kant, Logik, §.31. 



H 2 



100 ARTIS LOGICS 

CAP. IV. 
De Syllogismls Hypotheiicis^, 

§. 1. Syllogismus Hypotheticus, est in quo una, 
duae, vel tres propositiones hypotbeticae. v. g. Si 
sapit, est beatus : Sapit ; ergo est heatus. Vel, Qui 
sapit est heatus : Si est Philosophus, sapit ; ergo Si 
est Philosophus^ est beatus. Vel, Si sapit, est beatus: 
Si est Philosophus, sapit ; ergo Si est Philosophus, 
est beatus. Nos de eo tantum loqui instituimus 
qui est caeteris usitatior, in quo nempe Major 
Hypothetical 

* Hypothetical syllogisms, in the present sense of the term, 
are not treated of by Aristotle. An exposition of them was 
first sketched out by Theophrastus, which was afterwards 
further developed by Eudemus and the Stoics. None of these 
works, however, have come down to us. A few notices may 
be gathered from the Greek commentators ; but our principal 
extant authority on the subject is Boethius. Of the crvWo- 
yiaixol e| vTrodeaecos of Aristotle, which Pacius has confounded, 
and M. St. Hilaire attempts to identify, with the hypotheticals 
of Theophrastus, some account will be given in the Appendix, 
note I. In the Prolegomena Logica, p. 211, I have given a 
theory of hypotheticals different from that commonly adopted 
by Logicians. Bnt that theory, though I believe it to be 
more accurate than that of Aldrich, differs too widely from 
his text to be admissible here. I have therefore transferred 
it to the Appendix, note I. 

^ This is the only kind of hypothetical syllogism in which 
the conclusion is categorical. If the minor premise, or both 
premises, are hypothetical, the conclusion is so too. A 
syllogism with all three propo?idons hypothetical was called 
by Theophrastus, di okov vnoB'^iKosy (Scholia, p. 179. a. 16.) 



RUDIMENTA. 101 

Propositio Hypothetica late sumta definitur^ Plures 
Categoricae per conjunctionem aliquam unitse, et 
conjunctio vocatur Copula; estque Conditionalis, 
Disjunctiva, Causalis" &c. ut apud Grammaticos ; 
unde totideni Hypotheticarum species, suis copulis 
cognomines. Sed ad Syllogismum non faciunt, 
Praeter Conditionalem, et Disjunctivam^ ; quarum 
exempla. Si sapit est beatus, Vel dies est Del nox. 

Conditionalis habit vim illativam. Unde Con- 
ditio ipsa, sive pars prior, quae est instar inferentis, 
Antecedens dici solet ; Assertio, sive pars posterior, 
quae ration em habet illatae, Consequens ; partiumque 
inter se connexio. Consequential, 

•= Causalis, e. g " Because A is B, C is D." This is, of 
course, only a hypothetical in the loose sense of the above 
definition. In the same sense were admitted temporal hypo- 
theticals, "When A is B, C is D ;" locals, "Where A is B, 
C is D," &c. &c. The causal hypothetical proposition is really 
a curtailed hypothetical syllogism. " Because A is B, C is D," 
is equivalent to "If A is B, C is D, and A is B." Cf. Hoff- 
bauer, Logik, §. '^86. 

^ Nothing can be more clumsy than the employment of the 
word conditional in a specific sense, while its Greek equivalent, 
hypothetical, is used generically. In Boethius, both terms are 
properly used as synonymous and generic ; the two species 
being called conjiinctivi, conjuncti, or connexi, and disjunctivi, 
or disjunctL Cf. Edinhuryh Review, No. 115, p. '219. Boethii 
Opera, p. 610. The nomenclature of Boethius is followed by 
Ramus. With reference to modern usage, however, it will be 
better to contract the Greek w^ord than to extend the Latin 

I one. Hypothetical, in the following notes, will be used as 

I synonymous with conditional. 

\ ^ It has been questioned whether Hypothetical Syllogisms 

I can be reduced to Categorical. This question must not be 



102 ARTIS LOGICiE 

Conditionalis cujusque sententia est, quod, data 
Conditione, datur Assertio ; quod bifariam explicari 



confounded with the inquiry, whether the hypothetical pro- 
position is formally the same with the categorical. The latter 
is answered by Kant in the negative, but that decision does 
not affect the present question. The reduction of hypothetical 
syllogisms must be governed by the same rules as that of 
categoricals ; and in the latter case, it is allowable to substitute 
for a given proposition another which, though not identical, is 
implied by it. For instance, a particular converse is employed 
instead of its universal exposita. So in hypotheticals, if the 
new propositions contain the same terms, and are immediately 
deducible from the original ones, the reduction is legitimate. 
This will generally be the case when the hypothetical pro- 
position has but three terms ; both clauses having the same 
subject or the same predicate. The following instances may 
thus be reduced : — 



r All B is C, 

to I All A is B; 

I .-. All A is C. 

All A is B, 

All C is A ; 

.-. AUG is B. 



to . 



I. If All A is B, All A is C) 
But All A is B ; 
.-. All A is C. 

II. If All A is B, All C is B, 
But All A is B; 
.-. All C is B. 

These syllogisms, indeed, were admitted by the Ramists, 
the great advocates of hypotheticals, to be categorical. But 
where the hypothetical has four terms, as, " If A is B, C is 
D," this mode of reduction is not practicable; yet even in 
this case a categorical syllogism may be constructed, whose 
propositions, though expressed in different terms, are implied 
in those of the original syllogism. Thus : 

Constructive. Destructive. 

Every case of A being B, is a Every case of A being B, is a 

case of C being D. case of C being D. 

This is a case of A being B. This is not a case of C being D. 
.-. This is a case of C being D. .-.Thisisnotacaseof A beingB. 
The above directions are all that can be given on the ordinaiy 



I 



RUDIMENTA. 103 

potest. 1. Si detur Conditio, danda est Assertio ; 
unde Regula prima: Posita Antecedente, recte 
ponitur Consequens. 2. Si daretur Conditio, 
danda esset K^?>eri\o\ unde Regula secunda : Sublata 
Consequente, recte tollitur Antecedens. 

Porro hoc unum statuit, Antecedente vera, veram 
esse Consequentem ; non autem ambas esse simul 
veras, aut simul falsas, aut una vera, falsam alteram : 
per illam igitur, sublata Antecedente, poni vel tolli 
potest Consequens ; aut posita Consequente, poni 
vel tolli Antecedens. Unde Regula tertia: Sublata 
Antecedente, vel Posita Consequente, nihil certo 
colligitur^ 

Conditionalis igitur Syllogismi duae sunt, nee 
plures, formulae. 

I. Quae vocatur Constructiva, 
Si C. D. tum K. A. 
Sed C. D. ergo K. A. 

theory of hypotheticals. The first method of reduction is 
only approximately true ; and various ingenious examples 
have been framed by Logicians, to which it is inapplicable. 
See Krug, §. 82. Fries, §. 62. The truth is, that the so-called 
hypothetical proposition is really the statement of a conse- 
quence, which is sometimes formal, sometimes material ; and 
in the latter case, the consequence is extralogical, and cannot 
be reduced to any logical form, without additional assump- 
tions, derived from the matter treated of See Prolegomena 
Logica, p. 21 J. Appendix, note I. 

I ' By adopting the adove modes of reduction it may easily 

be seen, that the violation of this third rule is equivalent, in 

! the case of denying the antecedent, to an illicit process of 

I the major term ; in that of affirming the consequent, to an 

! undistributed middle. 



104 ARTIS LOGICiE 

II. Quae dicitur Destructiva^, 

Si CD. turn K.A. 

Sed non K. A. ergo non C. D. 

§.2. QuiE de Conditionali dicta sunt. Disjunctives 
satis cavent. Ejus enim in Syllogismo positae 
sententia conditionaliter efferri semper potest \ 

s The destructive syllogism is naturally reduced to the 
second figure in the categorical form, and cannot in most 
cases be brought to the first without considerable awkward- 
ness. This may be avoided by converting the hypothetical 
before reduction. A hypothetical proposition is converted by 
Contraposition ; thus, " If A is B, C is D," to, " If C is not D, 
A is not B." The syllogism may then be treated as a con- 
structive. Cf. Hamilton on Eeid, p. 697. Whately's Logic, 
b. ii. eh. 4. §. 3. 

Hypothetical as well as Categorical reasonings may be 
combined in a Sorites. The Hypothetical Sorites consists 
of a series of propositions, in which the consequent of each 
is the antecedent of the next ; the conclusion being composed 
of the first antecedent and the last consequent. Thus : 
Constructive Sorites. Destructive Sorites. 

If A is B, C is D. If A is B, C is D. 

If C is D, E is F. If C is D, E is F. 

If E is F, G is H. If E is F, G is H. 

.-.If A is B, G is H. .-. If GisnotH,AisnotB. 

See Wolf, Phil. Rat. §. 470. 

^ With regard to the import of the disjunctive proposition, 
Logicians are at issue. The majority (Kant among the 
number) regard it as stating all possible cases ; so that one 
only of its members can be true. And Aquinas maintains 
that any disjunctive proposition in which this condition is not 
observed, is false. On this supposition all the four inferences 
given by Aldrich are valid. But it may be questioned whether 
the incompatibility of the members appears in the form of 



i 



RUDIMENTA. 105 

V, g. Si posita vel C vel D 

Subsumatur 
Sed C ergo non D 

D non C 

non C ergo D 

non D C 

Pro exposita Disjunctiva 
die conditionaliter 



every disjunctive proposition. We may happen to know that 
two alternatives cannot be true together, so that the affirmation 
of the second necessitates the denial of the first, and the 
affirmation of the first the denial of the second ; but this, as 
Boethius observes, is a material, not a formal consequence, 
whether it be stated in the hypothetical or disjunctive form. 
It must be allowed that the examples sometimes adduced on 
this side of the question have not been very happily chosen. 
It sounds oddly enough to state a known truth as a possible 
falsehood, as in the instance, " Bellum Trojanum cecinit vel 
Homerus vel Virgilius.'" But other and more natural specimens 
have been given ; e. g. " Aut olim Troja fuit, aut historia de 
hello Trojano est merafabiila." The case is still clearer when 
both members of the disjunctive are negative, as in the 
example given by Boethius, " Si enim quis dicat, aut non 
est album aut non est nigrum, sive album non esse as- 
sumpserit, non necesse erit esse vel non esse nigrum ; sive 
nigrum non esse assumpserit, ut sit vel non sit album, nullam 
faciet necessitatem." On this supposition only two of the 
above syllogisms are valid, which may be reduced to hypothe- 
ticals as follows : 

Constructive. Destructive. 

If A is not B, C is D. If A is not B, C is D. 

But A is not B. But C is not T>. 

.-.CisD. .-. AisB. 

For a further account, see Wallis, Log. Thes. 2. 



106 ARTIS LOGICiE 

Si C turn non D 
D non C 
non C turn D 
non D C 

§. 3. SuPEREST Syllogismus quidam Hypothe- 
ticus redundans^ alio nomine Dilemma' y quia ple- 

' Of the word Dilemma, various etymologies have been 
proposed; 1. a choice of alternatives offered to an adversary; 
2. a double premise assumed (X^/x/xa) ; 3. a not veiy probable 
one given by Keckermann, " a Sis Xafi^dveaOai, quia utrinque 
capit et constringit adversarium contra quem adducitur." The 
first seems to be adopted by Aldrich, and is perhaps supported 
by Cassidorus, Expos, in Ps. 138, 9. "Dilemma, quod fit ex 
duabus propositionibus pluribusve, ex quibus quicquid electum 
fuerit, contrarium esse non dubium est." Cf. Victorinus in 
1 Rhet. Cic. 86. But whatever be the origin of the word, it 
was certainly employed as synonymous with the complexio of 
Cicero, (de Inv. 1. 29.) This is expressly stated by Servius, 
(on ^n. ii. 675.) who is, I believe, the oldest extant writer in 
whom the word is found. In this sense it may be defined, 
(omitting the adversary, as belonging rather to Rhetoric or 
Dialectic than Logic,) " A syllogism, having a conditional 
major premise with more than one antecedent, and a dis- 
junctive minor." Its different forms may be thus exhibited : 

I. Simple Constructive. 
If A is B, C is D ; and if E is F, C is D ; 
But either A is B, or E is F ; 
.-. C is D. 

II. Complex Constructive. 
If A is B, C is D ; and if E is F, G is H ; 
But either A is B, or E is F ; 
.-. Either C is D, or G is H. 



\ 



RUDIMENTA. 107 

rumqiie duo (etsi interdum plura) proponit adver- 
sario capienda ; quorum utrumvis acceperit, causa 
cadet. Tale est illud Biantis, Si uxorem ducas 
formosam, hahebis KOLvr]v, communem; si deformem, 
TTOLPTji/, poenam : ergo Nulla est ducenda^, 

^Hoc non valet, nisi ita comparetur, ut partem 
alteram accipi sit necesse ; utraque autem feriat ; 
nee possit retorqueri. Quae si vidisset Bias, suo 
sibi Dilemmate minus placuisset ; neque enim vel 
formosa uxor vel deformis necessario futura est ; 
sed est media qusedam pulchritudo, quam Ennius 



III. Destructive, (always Complex.) 
If A is B, C is D ; and if E is F, G is H ; 
But either C is not D, or G is not H ; 
.*. Either A is not B, or E is not F. 

There cannot be a simple destructive Dilemma of this kind, 
as is shewn by Abp. Whately, Logic, b. ii. ch. 4. §. 5. 

There is another form of reasoning, sometimes called 
Dilemma, which is also a hypothetico-disjunctive reasoning, 
but which, instead of having the major premise hypothetical 
and the minor disjunctive, has both combined in the major; 
the whole of the disjunctive consequents being denied in the 
minor, E. g. " If A is B, either C is D, or E is F ; but 
neither C is D, nor E is F; therefore A is not B." This 
foi-m is given by Wallis, lib. iii. cap. 19.; as well as by Wolf 
and Kant. But it is a perversion of the Dilemma proper, and 
introduces no distinction whatever ; being merely a common 
disjunctive syllogism, as is shewn by Wallis himself. It is, 
in fact, the enumeratio, not the complexio, of Cicero. 

^ See Gellius, Noct. Att. v. 11. 

^ These remarks entirely relate to the matter, and have 
nothing to do with the Logical character, of the Dilemma. 
See Whately, ii. 4. 5. 



108 ARTIS LOGlCiE 

statam appellavit ; Favorinus eleganter iixoriam. 

Porro, nee formosa omnis est communis, nee 

Arist.Rhet. deformis, poena. Denique Dilemma faeile retor- 

II 23 15 

queri potest. Puta, Si formosam duxero, non 

hahebo pcenam ; si deformem, non hahebo communem. 

Dilemma nihil aliud est, quam Inductio Nega- 

tiva"^ ; in qua Syllogism! Major Conditionalis est 

"^ This remark is taken from Wallis, and is only applicable 
to the Dilemma in his sense of the term. The negative 
induction appears categorically in this form : 

There are no instances of C being D, nor of E being F. 
But these are all the possible instances of A being B. 
.'. There is no instance of A being B. 

The Dilemma of Aldrich cannot, as it stands, be reduced to 
this form. The categorical conclusion, e. g. Nulla uxor est 
ducenda, does not follow from the premises of the Dilemma 
of Bias ; but requires the additional assumption, that neither 
matrimonial nuisance is, under any circumstance, to be 
endured. This brings it to Wallis's form, thus : 

Si duceyida est uxor, aut formosa ducenda est, aut deformis: 

Atqui non est ducenda formosa, neque deformis: 

Ergo, Uxor non est ducenda. (Burgersdyck, Inst. Log. ii. 13.) 

The Complex Dilemma, as given above, may be reduced, 
if required, to a series of hypothetical syllogisms, and so to 
categoricals : thus : 

Constructive. Destructive.. 

If E is F, G is H ; If E is F, G is H ; 

If A is not B, E is F ; If C is D, G is not H ; 

.-. If A is not B, G is H. .-. If C is D, E is not F. 

If C is not D, A is not B ; If A is B, C is D ; 

.-. If C is not D, G is H. .-. If A is B, E is not F. 

The reduction of the simple Dilemma is obvious enough. 



RUDIMENT A. 109 

cum consequente distributiva : puta. Si omnino, 
turn sic, vel sic, vel sic; quam afferre Categorice 
adeo est proclive ut non indigeat prsecepto. 

But all such reductions, except as serving to vindicate the 
universality of the syllogistic model, are rather curious than 
useful. 



110 ARTIS LOGICiE 



CAP. V. 

De Syllogismo quoad Materiam, 

§. 1. HtEC de Syllogismo quoad Formam spec- 
tato. Jam de eodem quoad Materiam, h. e. Certi- 
tudinem et Evidentiam proposition um ex quibus 
componitur. 

Certa autem propositio est, cui nihil occurrit 
in contrarium, vel quod occurrit instar nihili est; 
ut, Omnis homo est risibilis^ : Evidens, quae simul 

a This definition is vague enough : the example, however, 
shews more clearly what is intended. For risihile was regarded 
as a property, flowing from, and demonstrable by, the dif- 
ferentia rationale. We may therefore define a certain pro- 
position as " a proposition capable of demonstration." It 
will thus be distinguished from an evident proposition, which 
is axiomatic and indemonstrable. Both are, of course, 
necessary, which is essential to demonstrative reasoning : 
but the former is the conclusion of a demonstration ; the 
latter, a premise. Waiving the physical question of the 
necessary connection of risibility and rationality, we may 
give as examples, of a certain proposition, " The angles of 
every triangle are equal to two right angles ;" of an evident, 
" Things which are equal to the same are equal to each 
other." 

Such seems clearly to be Aldrich's meaning in the present 
passage ; in which certa and evidens correspond to what are 
commonly called immediata immedietate subjecti, and immediata 
immedietate causa. (Cf. Sanderson, lib. 3. cap. 12. from whom 
this part is chiefly taken.) Aldrich's subsequent language, 
however, is by no means consistent. 






RUDIMENTA. Ill 

ac percipitur assensum imperat ; ut, Totum est 
ji majus sua parte: Dubia, in qua haeremus, cum 
j illius pars utraque valde se probet intellectui ; ut, 
I Astra regu7it homines ; nam et regere et non regere 
i videntur. 

j Dubitanti siquid aliud occurrat, quo pendens 
animus in alterutram partem propendeat, quod 
erat Dubium fit Probabile^, Et potest, quod pro- Top.i.i.3. 
batur, Verum esse, sed probanti tantum Verisimile 
est. Multis nihilominus assentimur isto modo, et 
assensui nomen est Opinio^ 

Est igitur Opinio propositionis tantum probabilis; An. Post. 
eique nulla competit certitudo ; sed in ipsa sui 
ratione includit formidinem oppositi. Sunt Opi- 
nioni tarn en Gradus quidam ad certitudinem, pro 
diverso pondere rationum quae assensum movent, 
diversi. Est quod omnibus, quod plerisque, quod Top.i. 1.3. 
sapientibus videtur ; et quod horum singulis, quod 
plerisque, quod celeberrimis ; quorum omnium 
dispar est probabilitas ; quorumdam vero tanta, 
ut ad certitudinem quam proxime accedat. 

§. 2. Qui Opinionem (h. e. assensum quemlibet 
scientia minorem) parit, Syllogismus appellatur 

^ "'EvSo^a de ra doKOvvra Traaiv rj toIs TrXeiVrois fj rols aocfyoi^y Kol 
TovTOLs 1) TTaaiv ^ Tols TrXelarois ^ toIs /xaXtora yvoapi^OLs Koi ivbo^ois. 
Arist. Top. i. 1.3. Such propositions form the premises of 
dialectical syllogisms. 

'^ Aeinerai So^av eivai nepl to dXrjBes fxev 77 ylrev8os, ivbc\op.€Vov oe 
KoX aK\a>s ex^iv- Tovto d' earit/ vnoKrf^is rrjs dfxe<Tov Trpordcreas Koi firi 
dvayKaias. Anal. Post. i. 33. 2. 



!!k 



■S f 112 ARTIS LOGICS 

in 

M^ T:oip.i. \.^. Dialecticus, AiaXeKrcKo^^, i. e. probabiliter disse- 
^^ rens : quaeque proprie dicitur Dialectica, est pars 

Logicae quas de hoc agit Syllogismo. Multiplex 
autem est materia circa quam versatur opinio, et 
per omnes sparsa disciplinas : cujus infinitam pene 
varietatem ad pauca capita revocavit Aristoteles, 
et sub iis EfFata Dialectica suis quasi in sedibus 
locavit, Hapc itaque capita, Tottous-^ i. e. Locos 
appellat ; unde Syllogismus Dialecticus alio nomine 
Topicus dicitur ^ 

De Locis Dialecticis et ad ea pertinentibus 
EfFatis, sive (ut Scholastici vocant) Maximis^; 

^ AiaXe/crtKos de (rvWoyiaixos 6 i^ ivbo^cov avKkoyi^oixevos. Top. i. 
]. 2. On the origin and different uses of Dialectic, some 
remarks will be found in the Introduction. Its name had 
originally reference, not to the probable character of the 
matter, but to the colloquial form. 

® The TOTTOL are general principles of probability, standing in 
the same relation to the dialectic syllogism as the axioms to 
the demonstrative. A definition is given, Ehet. ii. '26. 1. eart 
yap (TTOix^'iov Koi tottos els o iroWa evdviirjiiaTa efxnLTTTei. The origin 
of the name may be illustrated by calling it the place in which 
we look for middle terms ; with which may be compared 
Cicero's definition, Top. ch. 2. " Itaque licet definire, locum 
esse argument! sedem : argumentum autem, rationem, quae 
rei dubiae faciat fidem." Cf. De Orat. ii. 174. Theophrastus' 
definition is given by Alexander, Schol. p. 252. a. 12. ea-n yap 
6 TOTToSf o)s \eyei Q€6(f)pao-Tos, apxv Tf^s V (^roixelov, dcf)' ov Xafi^dvofiev 
ras irepX eKaarov dpxds. 

^ The Schoolmen divided Loci into two kinds, which they 
called MaximcB, and DiferenticB Mammarum. The former were 
propositions expressing a general principle of probability, (or 
even of certainty, for the term was extended to include axioms;) 
such as, " De quocunque prsedicatur definitio, et definitum." 



RUDIMENTA. 113 

plura non loquor. Pro exemplo tamen hoc accipe : 
j Inter Maximas Loci primi, qui est Testimonium, T^oip. ul 
! reperitur haec ; Peritis credendum est in sua arte : 

ex qua elicitur hujusmodi Syllogismus Topicus. 
; Quod (Pythagoras) Ipse dixit concedendum est: 

Migrare animas Ipse dixit ; ergo Migrare animus 
\ concedendum est, Probatur Major; quia Peritis 
I credendum est in sua arte, 

§. 3. Certitudo eadem videtur, quae improprie 
vulgo dicitur Evidentia Moralist; quaeque iis con- 

The latter consisted of one or more words, expressing the 
point in which one maxim differed from another; e. g. the 
above maxim is said to be ex dejinitione et definito : so in 
Aldrich's example the maxim is, Peritis credendum est in sua 
arte; the differentia, Testimonium. The latter were sometimes 
called simply Loci. Cf Petr. Hisp. Tract, v. The distinction 
is not warranted by Aristotle, with whom the tottoi are always 
Propositions. 

The history of the word Maxim is given in a learned note 
by Sir W. Hamilton, Reid's Works, p. 766. He shews that 
it originated with Boethius, by whom, however, it was merely 
used as an adjective, in the phrase maxima propositio. The 
Schoolmen dropped the latter word, and employed maxima as 
a substantive. 

« This paragraph, Aldrich appears to have taken from the 
Cartesians, and spoiled in the taking. Thus Clauberg, Logica, 
P. I. qu. 133. " Quaenam axiomata minimum habent veritatis 
seu certitudinis ? Contingentia seu contingenter vera, h. e. quae 
ita vera sunt ut falsa esse possint: ut si judicem matres amare 
liberos suos. Horum axiomatum certitudo vocatur vulgo 
Moralis, non quod in rebus tantum ethicis seu moralibus 
locum habeat, sed quod aliter de talibus statuendo contra 
bonos mores plerumque peccetur." And in the same manner, 

I 



114 



ARTIS LOGICiE 



venit efFatis, de quibus nemo prudens dubitaverit : 
qualia praesertim sunt Principia ad vitam moresque 
pertinentia^ cum conclusionibus quas ab his legitime 
deducunturo Nam hujusmodi propositiones viden- 
tur esse plusquam probabiles^ nondum tamen 
evidentes : neque enim eas quisque amplectitur 
quamprimum apprehendit ; sed iis prudens sine 
ulla formidine assentitur. 

Certitudo^ duplex est ; alia Objecti, quae est rei 

moral certainty is distinguished from metaphysical by Descartes. 
Metliode, p. iv. This is obviously a totally different sense of jj 
the word certainty from that given at the beginning of the 
chapter. " Omnis homo est risibilis" can hardly by any 
stretch of language be called a moral precept. Moral certainty ^ 
is a very different thing from demonstrative certainty, being !- 
merely a high degree of probability. But nothing can be more 
confused than the whole of this chapter. 

^ We have now got back again to demonstrative certainty. 
This part is taken from Sanderson, whose account is infinitely 
clearer than that of Aldrich. " Demonstratio est Syllogismus 
faciens scire. Scire autem unumquodque dicimur, cum causam 
cognoscimus propter quam res est, quod illius rei causa sit, 
nee possit res aliter se habere. Unde duplex oritur scientiss 
certitude : altera objecti, vel scibilis, quando rei causa proxima 
apprehenditur : altera subjecti, vel scientis, quando sciens 
certus est rem non posse aliter se habere. Per illam dis- 
tinguitur scientia ab errore: per hanc ab opinione, quae includit 
in ratione sui formidinem oppositi." From the above account 
it is clear that there can be no degrees of either Certainty. 
For any obstacle as regards the object, renders the proposition 
no longer certain, but doubtful ; any consciousness of such in 
the subject, reduces the state of mind from knowledge to 
opinion. The same may be said of Evidence, in the proper 
limitation of the term. A proposition not sponte perspicuum 
may be certain, but is not evident. ^ 



I 



RUDIMENTA. 115 

percipiendae ; alia Suhjecti, quse est Intellectus 
percipientis'. Et utrique sui sunt gradus. Est 
enim Certius certitudine Objecti, id cui minus 
obest ; certitudine Subjecti, cui quod obsit minus 
percipitur. Evidentia similiter duplex est ; Objecti 
nempe, et Suhjecti; et utrique sui sunt gradus, 
Dispar enim evidentia est, prout id quod percipitur 
vel est sponte perspicuum ; vel a sponte perspicuo 
propius abest ; vel utrumvis horum videtur, 

Atque hinc, rursus. Evidential multifariam divi- 



i On the history of the terms Object and Subject, Objective 
and Subjective, see Sir W. Hamilton's note, Beid's Works, 
p. 806. and Trendelenburg, Elementa, §. 1. The variations 
between the scholastic and the modern sense of these terms 
are however in this particular relation unimportant. Where 
knowledge or certainty is spoken of, the subject of inherence 
(in the scholastic sense) is the mind as knowing; and the 
object proper is the thing as known ; and thus far, the 
modern use of the same terms is nearly coincident ; though 
when viewed out of relation to the act of knowledge, the two 
nomenclatures are exactly the reverse of each other. In our 
present point of view we may distinguish certitudo objecti as a 
quality of the proposition as apprehended by the mind, and certi- 
tudo subjecti as a state of the mind as apprehending the proposition; 
and in this sense the two are inseparable from each other, 
being only the same act of thought viewed from opposite 
sides.. This is the only sense of object and subject with 
which Logic has any concern. The subjective existence, as the 
schoolmen would call it, or the objective existence, as the 
moderns would call it, of things out of the act of thought, 
belongs to a metaphysical inquiry, with which, as Logicians, 
we have no concern. 

^ Evidence is here extended so as to include not only 
axiomatic but demonstrated propositions. This licence 

i2 



116 ARTIS LOGICS 

ditur. Sed nostro sufficit institute, quod haec, de 
qua loquimur, Propositionis Evidentia, vel est 
1. Axiomatis sponte perspicui ; cui proinde sine 
ulla probatione assentimur : vel 2. Conclusionis 
ab ejusmodi axiomatibus {immediate an mediate 
parum refert, modo) rite deductas. Nam cum 
una sit Veritas, sibi constans, apteque coh^rens ; 
quodque verum, vel per se certum atque evidens 
sit, vel cum efFatis quibusdam certis et evidentibus 
necessario connexum ; fit, ut quamprimum appre- 
henditur hsec connexio, eadem omnia quasi luce 
perfusa, parem (specie) consequantur assensum. 

An. Post. §. 4. Qui postremse huic evidentiae competit 

12 2 

I.' 4! 1*. assensus apud Logicos vocatur Scientia, Est igitur 
Scientia conclusionis certce et evidentis, a prsemissis 
certis et evidentibus legitime deductael Certitu- 
dinem vero utramque intelligo ; et utramque (tarn 
Objecti scilicet quam Subjecti) evidentiam. Nam 

An. Post, per Objecti certitudinem Scientia distinguitur ab 
Errore ; per Subjecti certitudinem ab Opinione^, 

Aldrich perhaps took from Crakanthorpe, who uses eertain 
and evident as synonj'raous terms ; but he departs from his 
principal authority, Sanderson, and is inconsistent with him- 
self. Evident should be limited to the axioms, the original 
premises of demonstration ; certain, to the conclusion. 

^ It would be better to say, "conclusionis certae, a prsemissis 
certis vel evidentibus." The premises in demonstration may- 
be axiomatic principles, or the conclusions of previous demon- 
strations. In both cases the result is scientia, though in the 
latter the demonstration is not potissima. 

"^ Strictly speaking, objective and subjective certainty of 



RUDIMENTA. 117 

Si desit evidentia subjecti, nulla est Scientia ; ubi 
sola adest, persuasa tantum, non realis evidentia 
est. 

Qui Scientiarn parit Syllogismus appellatur An. post. 
Scientificus ; alio nomine, * ATrodecKTiKo^ Demon-i.4.1. 

• . T ^ • ^ 1 • Top.Ll.2. 

strativus, et mterdum Demonstratio. Conclusiones 
enim certas et evidentes apud Mathematicos repe- 
riri multas in confesso est : cumque Illi, quae 

thought cannot be actually separated from each other, being 
merely tlie same act of thought viewed from opposite sides. 
Of objects out of the act of thought, the thinker knows 
nothing. But in comparing two minds together, one of 
whom is supposed to have a firm conviction of a true pro- 
position on sufficient grounds, the other an equally firm con- 
viction of a false proposition, the difference between them 
will lie, not in the state of conviction which is common to 
both, but in the object on which it is exercised; and the 
change from error to knowledge will be effected by the 
substitution of one object for another. On the other hand, 
if a truth known scientifically by one man is assented to with 
hesitation by another, the difference lies in their respective 
states of mind in relation to a common object, and the change 
from opinion to knowledge will consist in a different mode of 
contemplating the same truth. Hence, in strict accuracy, we 
should say, that the characteristic of error is the attribution 
of certainty to a wrong object; that of opinion, the absence 
of certainty in the subject. The criterion of knowledge from 
error is strictly the character of the object as it appears to a 
rightly informed mind ; and hence, among the later Logicians, 
we find respectu objecti used as equivalent to per se; and opposed 
to respectu subjecti, as it appears to this particular thinker. 
This forms the connecting link between the scholastic use 
of objective to denote what exists only in thought, and the 
modern use, to denote the absolute affections of things 
without the mind. 



118 ARTIS LOGICiE 

decent, soleant adjuncto Diagrammate ostendere ; 
seque propterea non rem probare, sed (quod 
majorem innuit Evidentiam) Demonstrare dicant; 
arcessito igitur ab illis vocabulo, Syllogismus scire 
faciens apud Logicos vocatur Demonstratio, Cum- 
que in Scientia (siqua forte possibilitas, tamen) 
nullus sit erroris metus ; quod hujusmodi Syllo- 
gismis, sive uno, sive pluribus probatur, id libenter 
agnoscimus sicut perhibetur ita esse; et aliter 
(saltern naturaliter) se habere non posse. 

§. 5. Du^ sunt Demonstrationis species. Prima, 

quae demonstrat Otl, sive Quod res sit; probando, 

vel simpliciter et directe rem ita esse, et tum 

Anal. Pr. vocatur Osteusiva, seu potius Directa ; vel si non 

An. Post! sit, absurdi aliquid necessario secuturum. Haec 

est quae Graece dicitur ^ ATraycoyrj'^ , Latine, ducens 

^ aTrayoyyfi' ducens ad impossibile. This is only a correct 
rendering of the Aristotelian diraycoyr) els t6 ddvvarov: see p. 86. 
note e. The term diraycoyr}, when it occurs by itself, has a 
different meaning. It is a syllogism whose major premise is 
certain, and its minor either more probable or more easily 
demonstrable than the conclusion. It thus holds an inter- 
mediate place between the demonstrative and the dialectic 
syllogism. See Anal. Pr. ii. 25. 

The connecting notion between these two senses of dTrayayyri 
seems to be that of a change of question ; a turning off from the 
immediate point to be proved to something else on which it 
may be made to depend. Thus, in the deductio ad impossibile^ 
instead of proving the original question directly, we attempt 
to shew the falsehood of its contradictory ; and in the present 
case we abandon the immediate proof of the conclusion for 
that of the minor premise on which it depends. 



I. 26. 1. 



RUDIMENTA. 119 

ad absurdum, impossibile, incommodum, uno verbo 
recte dixeris Obliquam, Exemplum ejus dat re- 
; ductio Syllogism i a Baroko vel Bokardo ad Bar- 
bara. 

Ostensiva Directa fit duobus modis. 
1. Quando aliquid demonstratur per Effectum ; ^n. Vosu 
j ut si diceres, Luna Soli opposita nigra ceriiitur , ' ' ' ^ 
ergo patiiur Eclipsin, 2. Quando per Causam au. Post. 
remotam; ut si idem colligeres quia Sol et Luna ' ' '"' 
diametraliter opponuntur. Quod si illud demon- 
■ strares per Causam proximam, quia nempe Terra 
inter Solem et Lunam interponitur y turn fieret 

Secunda Demonstrationis species A^ort, i. e. quae An. Post. 
docet Quare, vel Propter quid res sit; causam ii 10.4,6. 

II 17 3. 

ejus assignando, non quamcunque, sed proximam 
seu immediatam''. Sic enim statuunt Logici quod 



o Tmmediatam. The word aix^cros is used in two senses by 
Aristotle. 1. For a proposition not proved by any hiyher 
j middle term ; i. e. an axiomatic principle, forming the first 
premise of a demonstration. Such is the sense in Anal. 
Post. i. 2. 2. and ii. 19. 1. 2. For a premise immediate as 
regards its conclusion; i. e. not requiring the insertion of 
lower middle terms to connect its terms with those of the 
conclusion. Such is the sense in An. Post. i. 13. 1. This 
second sense is intended here. 

Of an immediate proposition in the first sense, the favourite 
scholastic example was, Omne animal rationale est risihile ; the 
predicate being regarded as flowing directly from the subject, 
not as connected with it by any intervening cause. Whereas 
in homo est risibUis, between predicate and subject intervenes 
the middle term rationalise See Aquinas, Opusc. 48. de 
Syll. Demon, cap. 5. Zabarella, in I. Anal. Post. c. 2. 



ir. 18. 



120 ARTIS LOGICiE 

Scientia omnis est Cog?iitio rei per causam, sed 
proprie dicta per propriam, h. e. proximam: nam 
per remotam Cur sit aliquatenus ostenditur ; nihil 
amplius quam Quod sit demonstratur. 

Utriusque Speciei membra gradu diiferunt. Nam 
obliqua ore est deterior directa, quia non demon- 
strat rem ita esse, nisi quatenus docet earn aliter se 
habere non posse; quod tametsi eodem redeat, 
tamen animo minus satisfacit ; nam si par sit 
utrobique Certitude, bujus tamen minor Evidentia 
est P. 
An. Post. Habet et Aiort suos gradus; quia potest esse 
causa proxima quae non est prima, h. e. per se 
nota et indemonstrabilis : cujus ideo praefertur 
Evidentia, quia (contra quam caeterae) sua luce est 
conspicua, et nihil indiget aliena. Quare, quae 



cont. 9. Hence the following specimen of a demonstratio 
potissima : 

Omne animal rationale est risibile ; 

Omnis homo est animal rationale; ergo 

Omnis homo est risibilis. 

Any subsequent demonstration from this conclusion ; e. g. 
Omnis Philosophus est homo; ergo Omnis Philosophus est 
risibilis; would be per causam proximam, sed non primam. 
Whether this distinction can fairly be traced to Aristotle is 
questionable. Some further remarks will be found, Appendix, 
note K. 

p Here we have a thu'd meaning of evidentia. It is now, 
not the evidentness of a Proposition, but that of a Demonstra- 
tion; i. e. the clearness of connection between premises and 
conclusion. 



RUDIMENTA. 121 

hanc adhibet causam demonstratio, et habetur, et 
nominatur Potissima, 

Sunt igitur ex mente Logicorum Demonstrandi 
quatuor modi; quorum alter alteri evidentia, adeo- 
que dignitate, prsestaf^. Falet Demonstratio obli- 
qua ; Potens est quaelibet Directa ; Potior quae per 
causam proximam, Potissima quae per primam 
demonstrat. Hujus est vulgata ilia Definitio, An. Post. 
Syllogismus constans veris, primis, immediatis, notio- 
ribus, prioribus, et causis Conclusionis^, Exem- 
plum, nisi forte apud Mathematicos, an uspiam 
occurrat nescio. 



*i The following table may assist the learner. 

Demonstratio 
I 



Quod sit Propter quid sit 
I I 



Obliqua Directa Non Potissima Potissima 



per deductionem 
ad impossibile 



per causam per causam 

proximam quae proximam et 

non est prima primam 



per effectum per causam 
remotam 

^ This definition is translated from Aristotle. ' KiroheL^iv de 
Xcyo) (TuXXoyicr/xoi/ eTTKTTrjfjLOViKou. '^TrcaTTjfxoviKov Se Xeyw KaB' op ra 
(f;(e«' avTov eTria-rdixeda. Et roiuvv earl to eTriaraadai olov Wey^ev, 
dvayKYj Koi ttjv dirodeiKTiK^v eTno-Trjixrjv e^ aKr]65>v t etvai Koi TrparoiV 
Koi dfxeo-cov Koi yvaypiixcorepcov Koi npoTepcov koi alricov tov (TvprnepdapLaTos. 

Anal. Post. i. 2. 2. See further, Appendix, note K. 



122 ARTIS LOGlCiE 



CAP. VL 

De Methodo'', 

§. 1. Methodus est talis dispositio partium ali- 
cujus disciplinae, ut Integra facilius discatur^ 

* MiOobos in Aristotle is employed with various shades of 
meaning; 1. for any instrument of acquiring or communicating 
knowledge; as in de An. i. 1.4. norepov aTrodei^is rls ea-nv ^ diai- 
p€(Tis Tj Kai Tts oKXtj fieOoBos. Cf. Philoponus, Scholia, p. '^35, a. 10. 

2. for knowledge reduced to system ; and thus as equivalent 
to ima-Tfjfir} : Phys. Ausc. i. 1. 1. Eth. Nic. i. 1. 1. Top. i. 2. 2. 

3. for a systematic treatise on any branch of knowledge, 
synonymous with irpayfiaTeia: Polit. iv. 2. 1. vi. 2. 6. Eth. Nic. 
i. 2. 9. But method, in the present sense of arrangement^ is 
not treated of in the logical writings of Aristotle, with the 
exception of a few rules for the arrangement (rd^is) of a dialec- 
tical disputation in the eighth book of the Topics. A lost 
treatise, called Methodica, is mentioned in the Rhetoric, I. 2. 
Method, as a distinct part of Logic, was first introduced by 
Ramus, and from him passed to the logical writings of the 
Cartesians and of Gassendi, by whom it was treated as a 
fourth part of Logic. Like most of the additions to the 
Aristotelian system, it was originally the property of the 
Rhetoricians. 

^ Method has been treated of by Logicians in two principal 
senses. 1. As a process of inference from the known to the 
unknown ; which is the earlier sense of the term, and sanc- 
tioned by Aristotle and his Greek interpreters. 2. As an 
arrangement of truths already known, with a view of com- 
municating them to others. The last corresponds to the 
Greek rd^is, and should rather be called Ordo. It is distin- 
guished from the first by Zabarella and others. Aldrich's 
definition corresponds only to the second sense of Methodus ; 
but in his subsequent division he confounds it with the first. 



RUDIMENTA. 123 

Estque duplex. 1. Inventionis, quae disciplinae Eth. Nic. 

praecepta invenit ; 2. Doctrines, quae tradit. Prior p'hys.Ausc. 
! procedit a sensibilibus, et singularibus, quae sunt 
I nobis notiora, ad intelligibilia, et universalia quae 

sunt notiora natures ; posterior^ contra ^ 



Method in either sense is not properly a part of Pure or 
Formal Logic. It is an application of Logic to the discovery 
or communication of truths in material science : its rules 
cannot be determined a priori from the laws of thought ; but 
must be gathered empirically from the examination of parti- 
cular sciences, and will require modification in many instances 
from the particular matter with which they have to deal. 

<^ The Methodus Inventionis can only be a process of inference : 
for no arrangemeyit of parts is possible before they have been 
discovered. The discovery of general principles from individual 
objects of sense, if limited to the inferential process itself, 
will be Induction. The term, however, is sometimes extended 
so as to include the preliminary accumulation of individuals. 
In this wider sense it will embrace the four successive steps 
given by Aristotle, Anal. Post. ii. 19. aiaOrjcns, iJ-vfifMrj, einrcipia, 
inayoiyrj. 

But the Methodus Inventionis must not be absolutely limited 
to Induction and its preliminaries, though these are the most 
important instruments of discovery. In some sciences, as in 
mathematics, truths are chiefly discovered by demonstration ; 
and, till so discovered, cannot, of course, be imparted to others 
by the methodus doctrines. 

Induction and Syllogism are the only two methods of 
inference. The Greek commentators, Ammonius and Eu- 
stratius, enumerate four, adding Division and Definition ; but 
in these last there is no reasoning process. See Zabarella, 
de Methodis, lib. iii. cap. 5 sqq. If we extend the method of 
discovery beyond the process of inference proper, so as to 
include any accumulation of knowledge, we may distinguish 
three principal instruments. 1. Pure experience, applicable to 



124 ARTIS LOGICS 

Methodus Doctrinae duplex est. ^Perfecta, aKpoa- 
IxaTLKT] ; et Imperfecta, e^corepLKr}. Perfecta rur- 
sus, vel Universalis est, qua Integra disciplina, vel 
Particularism qua aliqua disciplinae pars docetur. 
Utraque duplex est. 
An. Post. 1. Compositoria sive Synthetical, quae inservit 

L 10. 4. 

Eth. Nic. 

I. 2. 5. the acquisition of historical knowledge. 2. Demonstration, 

applicable to sciences of pure reasoning. 3. Induction, ap- 
plicable to mixed sciences of reasoning and fact. Cf. Fries, 
System der Logik, §, 117. 

^ The Methodus Doctrines is not in the same sense a process 
of inference from known to unknown ; for the parts are sup- 
posed to be known already to the teacher, and are methodically 
arranged for the benefit of the learner. This then corresponds 
rather to Order than to Method in the proper sense. It may 
be an arrangement either of the whole or of a portion of a 
subject; and is thus either universal or particular. Cf. 
Zabarella, de Methodis, lib. ii. cap. 20. The distinction 
between the Perfect and Imperfect Method is not usually 
recognised by writers on the subject. Aldrich is thinking of 
the acroaynatic and exoteric teaching of Aristotle and others ; 
the characteristic feature of the latter being the suppression 
of certain doctrines as not fitted for a promiscuous audience. 
Whereas the universal and particular Methods merely relate 
to the whole and the parts in the same exposition. 

e On Synthesis and Analysis, and the various employment 
of both, some remarks will be found in the Appendix, note G. 
The notion of Synthesis in the present passage corresponds 
to that of Metaphysical parts and whole, which is there men- 
tioned as applicable to a syllogistic process from a general 
principle to its particular application. Not so that of Analysis ; 
which in the present passage is also a process from the universal 
to the particular, not from the particular to the universal. 
By Suhjectum is meant the most general Subject whose pro- 
perties the Science investigates ; as Magnitude in Geometry^ 



RUDIMENTA. 125 

disciplinis Theoreticis ; et a notione Suhjecti 
\ incipiens, principia ejus et species investigat, 
donee a summo genere in ista disciplina per- 
veniat ad infimam speciem^. 2. Resolutoria siveEth. Nic. 
Analytical, quae inservit disciplinis Practicis ; etvii. 9!4. ' 

Metaph. 
VI. 7. 6. 
The Principia are the apxaX i^ hv, or axiomatic principles, from 
which the demonstration commences. Species are the sub- 
divisions of the general Subject; as the square, the triangle, 
&C. Cf. Anal. Post. i. 10. 4. liaa-a yap dnodeLKTiKr) eTno-Trjfirj nepl 
rp'ia iuTLV, ocra re elvai Tiderat [ravra S' earl to yevos, ov to)v koB* avra 
iraOrjfjLaTcov ia-Ti deojprjTLKrj ) kol to kolvo. Xeyoiieva d^iaiJiaTa, i^ hv Trpoirav 
a.7rodeiKvv(Ti, koi rpiTov ra TrdOrj, hv tI (rrjfiaLvet eKaarov Xofi^dvei. On 
the position of these in demonstration, some remarks will be 
found in Appendix, notes C and K : see also Trendelenburg, 
Erlauterungen, p. 118. 

^ " Exemplum evidens in primis est in scientia physica, 
I ubi primum tractatur de corpore naturali in genere, deque 
affectionibus ejus et principiis; post descenditur ad species 
corporis naturalis, videlicet corpus simplex, coelum, ele- 
mentum ; post mixtum, idque iterum vel imperfecte mixtum, 
vel meteora; post perfecte mixtum, idque iterum vel in- 
animatum, ut metalla, mineralia, vel animatum, idque vel 
vegetans, ut planta, vel sentiens : idque iterum vel irra- 
tionale, ubi tractantur omnia animalia bruta: vel rationale, 
ut homo; atque ita a summo genere ad species infimas 
devenitur. Eadem methodus observatur in mathematica et 
physica." Keckermann, Syst. Log. lib. iii. Tract, ii. cap. 1. 
Cf Zabarella, de Meth. lib. ii. cap. 7. 

s The Analytic, as well as the Synthetic Method, observes 
a deductive order from premises to conclusion. Its name 
then refers, not to the metaphysical relations of Species and 
Genus as whole and part, but to that common illustration of 
Aristotle's, by which, in productive or practical operation, the 
product or end is represented as a whole, and the materials or 
means as parts. The order of teaching will be the same as that of 
deliberation ; the reverse of that of operation. The following 



126 ARTIS LOGIC.*: 

a notione Finis incipiens, subjectum, et tandem 
media mvestigat\ 

Regulse Method! generales hag sunt. In tra- 
denda disciplina 1. Nihil desit aut redundet. 
2. Singulae partes inter se consentiant. 3. Nihil 
tractetur quod non sit subjecto aut fini homo- 
geneum. 4. Singulae partes aptis transitionibus 
connectantur. 



passages may illustrate the image. Eth. Nic. iii. 5. 11. oKka 
Sefxevoi riXos ri, 7ra>s Koi 8ia riva>v ea-rai (TKOirovcn, Kat hia TrXeiovoav 
jxev (paivofievov yiveadat 8ia tlvos pacrra Koi KoiKXiara €7n(TK07rovcri, 8i 
evoy d' eTnTeXovfxevov ttcos Blo. tovtov earai KOKelvo 8ta rivos, ecos av 
eXBacriv em ro Trparov airtov, 6 iv rfj evpeaei ecrxarov ioTiv' 6 yap 
^ovXevopcvos eoiKC ^rjTeiv koX dvaXvetv aanep bidypap,p.a . . . koX to 
ea-)(O-T0v iv rfi dvaXvcrei TrpatTov iv rfj yevicrei. Etll. Nic. vi. 13. 10. 
ol yap crvWoyiar p.o\ tS)V TrpaKToov dpxrjv exoiTes elaiv, ineidr) roiovSe 
TO TeXos Kal TO apio-Tov. vii. 9. 4. iv bk Tois irpd^eai to ov eveKa 
dpxf} coo-Tvep iv roTs fiadrjp.aTiKo'is ai xmoQio-eis. An example of the 
deliberative and practical processes will be found, Metaph. 
vi. 7. 7. 

By subjectum is meant the subjectum operationis, or materia 
circa quam, more properly called the object; by media, the 
means by which out of this matter the end is produced. In 
building, e. g. the house is the end; the materials the subject; 
the act of building, the means. In Ethics, as treated by 
Aristotle, happiness is the end; man the subject; virtue the 
means. 

^ Exemplum evidens methodi analyticse ab Aristotele in 
Ethicis proponitur, ubi libro primo Jinis prsecognoscitur, 
scilicet felicitas; post subjectum, nimirum hominis appetitus, 
seu voluntas, et intellectus; sequentibus libris ?7iedia tra- 
duntur, per quae finis introducitur, videlicet virtutes theo- 
reticse et practicae." Keckermann, Syst. Log. lib. iii. tr. 2. 
cap. 1. 



RUDIMENTA. 127 

5. Praecedat in docendo, sine quo alterum intel- 
ligi non potest, ipsum vero sine altero potest. 

§. 2. In tradendis disciplinis suis Mathematici 
hac utuntiir methodo'. 1. Vocum significationem 
constituunt : h. e. Vocahula artis suo quodque loco 
sic definiunt, ut legem sibi statuant iis nusquam 
uti, praeterquam in eo sensu quern explicat defi- 
nitio. 2. Definitionibus subjungunt Axiomata, 
quas et kolvols ivvoias vocant-'; h. e. efFata sponte 
perspicua, quibus in decursu operis utendum vident. 

3. Posthaec adjiciunt Postulata, quae ad praxin 
spectant : suntque per se certa et evidentia ; quae 
proinde sine probatione concedi suo jure postulant, 

4. Hisce positis, propositiones demonstrant; ordine, 
et, quoad fieri potest, affirmate : una lege con- 
tenti, ut, quicquid demonstratum eunt, ex ante 
datis vel probatis manifestum faciant. Caetera, in 
quibus methodi praeceptores multi sunt et odiosi, 
non morantur. 



* Hac utuntur methodo. For a further account of the method 
of mathematical reasoning, see Appendix, note L, on the 
Logic of Geometry. 

J The KOLvai fvvotai of the Mathematicians correspond to the 
d^ioifxara of Aristotle. The latter term is not used by Euclid ; 
nor by any of the early Mathematicians in its Ai'istotelian 
sense. Among the Stoics, axiom was synonymous with pro- 
position, and in this sense it is mentioned in a passage of 
Apuleius, quoted p. 43, note a. For a full history of the term 
and its several uses, see Sir W. Hamilton's note, Reid's Works, 
p. 764. 



128 ARTIS LOGIC.E RUDIMENTA. 

Mathematicorum methodum in caeteris artibus 
et scientiis, si ten ere non liceat, aemulari certe 
licet. Quo ad banc quaeque proprius accedit, eo 
caeteris perfectior^ et ad docendum aptior videtur. 
Sed ad ea quae docentur retinenda^ nihil est utilius 
absoluti operis conspectu ; in quo^ ea quae sunt 
ante (extra ordinem fortasse) demonstrata, suis 
quaque in locis, h. e. servata Logicorum methodo, 
reponantur. 



I 



APPENDIX. 



Solutio Sophismatum *. 

§. 1. CujuscuNQUE Syllogism! difficultas ad duas 
Species revocari poterit ; alteram, quas in Argu- 
menti Materia, alteram, quae in Forma consistit : 
nam qui has duas expedire noverit, is in tertia, quae 
ex ambarum complexione oritur, non haerebit. 

* The examination of Fallacies is extralogical, except when 
the consequence is formally invalid ; in which case it may be 
detected by the ordinary rules of syllogism. The following 
Sophisms are not all susceptible of this solution. They are 
mostly material fallacies, arising from ambiguity of language 
or falsity of assertion. But they are not treated of by Aristotle 
as belonging to the Science of Logic, but to the Art of Dia- 
lectic, of which, as has been before observed, a considerable 
portion is material. In fact, Aristotle's Treatise Trepl a-ocfua-TiKav 
eXey^coj/ is merely an account of the pseudo-refutations prin- 
cipally in use among the Sophists of his day, whether depend- 
ing upon equivocal language, false assumption, or illogical 
reasoning. In relation to Logic, it has little more than a 
historical value. A strictly logical classification of fallacies 
should commence by distinguishing, in all the three operations 
of thought, between the matter which is given to, and the form 
which is given by the thinking act. Acts of conception, judg- 
ment, or reasoning which violate the laws of thought, and are 
therefore defective in form, should be classed as logical fal- 
lacies ; those which are faulty in the conditions preliminary 
I to the act of thought should be classed as material. See 
I further, Prolegomena Logica, p. 237. and below, Appendix, 
i note M. 



130 



APPENDIX. 



Soph. Si incident Materia difficilis, unicum huic malo 

9. 1. remedium est, disciplinam unde desumitur argu- 
mentum, fideliter didicisse ; quod ut facias, Instru- 
menti operam tibi Logica pr^stabit ; sed ulterius 
nihil confert. Proprium illi munus est Syllogismi 
Fornnam explorare ; h. e. Utrum Conclusio ex 
Praeniissis consequatur propter ipsum Colligendi 
modum : Sed an ponendje sint Praemiss^ (nisi 
forte sint pure Logicse) aliunde discendunri est. 
Sicubi autem Syllogismus qui legitimus non est, 
videatur tamen ; aut contra ; (quorum utrumque 
saepissime, et de causis peue infinitis accidit) For- 
nialem ejus Consequentiam excutere est Artis 
Logics. 

Qui hoc opus aggreditur, id sibi negotii datum 
sciat, ut Difficilem suum Syllogismum, primo in 
Categoricum purum, vel in plures, si opus sit, con- 
vertat ; tum ad Canonem accurate exigat ; cujus 
operis ratio praecedente Libro abunde declarata 
An. Pr. I. est. Summa rei hue redit. Consideranda est 

32. 8. 

primo Conclusio ; ejusque Termini solerter dis- 
tinguendi : Prsedicatum enim est Major Terminus 
Syllogismi ; qui proinde Praemissam quoque Ma- 
jorem indicabit ; Subject urn pariter Minorem ; et 
in utraque sese offeret Argumentum sive Terminus 
Medius : Unde et si desit Prsemissarum alterutra, 
facile suppleri poterit. Hisce cognitis, nee Figura |: 
Syllogismi, nee Modus latebit ; qui si legitime, necli 
tamen vere concludere videatur, quaerendum annonjf 
aneeps sit aliquis trium Terminorum ? nam si in iis 



f 



APPENDIX. 131 

nulla lateat ambiguitas, necessario falsa erit altera 
Praemissarum, 

Hunc in modum licebit Syllogismum quemvis 
Categoricum purum explorare ; qualis si non sit 
qui proponitur, quam facillime fiet, per ea quae 
priore Libro, extremo Capite tertio^ et toto quarto 
sunt ostensa. Siquid amplius restet, id Exemplis 
melius quam Praeceptis docebitur. 



§. 2. Ordiemur autem a facillimis ; nempe vete- Soph. 
rum Sophistarum Fallaciis ; quarum 13 species 4.1. 
enumerat Aristoteles ; sex, qua? multiplicitate die- 
tionis ; septem, quae aliquo extra dietionem vitio 
laborarent^ Et erat aliqua fortasse difficultas in 

'' Of the Aristotelian division of Fallacies into oi napa Tr]v 
ki^Lv and 01 e^o) T^? Xe^ecos, Arclibishop Whately observes, that 
it has not hitherto been grounded on any distinct principle : 
he therefore adopts a conjectural explanation, according to 
which the former are interpreted as logical Fallacies, in which 
the conclusion does not follow from the premises ; the latter, 
as material Fallacies, where the conclusion does follow, the • 
falsehood being in the assumption. This, however, is not 
the ancient principle of distinction, which is stated, with 
more or less clearness, by several Logicians. To go no 
higher than Sanderson; we find, " Fallacia omnis in dictione ; 
oritur ex dictionis aliqua multiplicitate. Est autem Multiplex 
aliud actuale : quando dictio invariata multa significat ; ut in 
cequivoeatione, et amphiholia. Aliud potentiale : quando dictio 
quoad prolationem aliquo modo variata, multa significat ; ut 
in compositione, divisione, et accentu. Aliud phantasticum : 
quando dictio unum reipsa significans, videtur tarn en multa 
significare ; ut in jigura dictionis. Fallaciae extra dietionem 
sunt in quibus contingit deceptio, non tarn ex multiplici 
aliquo latente in vocibus ipsis, quam ex ignoratione rerum." 

k2 



132 APPENDIX. 

earum aliquibus, juxta veterem disputandi (h. e. 
interrogandi) morem propositis; sed profecto nemo 
tarn obtusus est, qui non easdem Syllogistice pro- 
positas agnoscat statim, et derideat. V. g. Erit for- 
tasse qui rogatus Quod non amiserit iitrum habeat 
necne? non intelligat se captum iri, sive simpliciter 
habere se, sive non habere respondent: at proposito 
hujusmodi Syllogismo, Quod non amisisti hahes ; 
Cornua non amisisti; Ergo hahes: Vel Quod non 
amisisti non hahes ; Oculos non amisisti ; Ergo non 
hahes ; quid reponat nemo non videt. 



This principle is found in Alexander of Aphrodisias, Scholia, 
p. 298, b. 28.; and still earlier, if the work be genuine, in the 
Treatise Trepl rav wapa rrjv Xe^iv aofjuo-fj-dTcov, ascribed to Galen. 
Indeed it may be gathered from Aristotle himself; Soph. 
Elench 4, 1. 6, 2. 7, 3. Occam states the distinction still 
more clearly. " Fallaciae in dictione sunt illse penes quas 
secundum omnes modos peccant sophistica argumenta com- 
posita ex signis voluntarie institutis. Fallaciae extra dictionem 
sunt illae penes quas peccant argumenta tam composita ex 
signis voluntarie institutis quam composita ex signis naturali- 
ter significantibus." Logica, iii. 4. cap. 1. The former arise 
from defects in the arbitrary signs of thought, and hence are ' 
generally confined to a single language, and disappear on ■. 
being translated into another. The latter are in the thought ^ 
itself, whether materially, in the false application of notions I 
to things, or formally, in the violation of the laws by which 
the operations of the reason should be governed; and thus 
adhere to the thought, in whatever language it may be ex- 
pressed. Under this head are thus included both false 
judgments and illogical reasonings. These Fallacies are 
connected with language only secondarily and accidentally; 
the former primarily and essentially. See further, Waitz, 
vol. ii. p. 582. 



i 



i 



APPENDIX. 133 



Fallaciae dictionis, sive m dictione, sex sunt*". 
§.3. 1. Fallacia cequivocationis, sive iiata ex Soph. 

. ^ . . , o. • Elench. 

voce aeqmvoca: ut. Cams est animal; iSirius est 4.. i. id. i. 
canis ; Ergo, Sirius est animal. In hoc quatuor 
sunt termini ; quorum duo, vox Canis aequivoce 
sumpta. 

2. Fallacia amphibolice ; sive nata ex sententia Soph. 

... ^7 Elencli. 

ampnibola, h. e. ancipitis structurae ; ut Qiwd tan- 4. 4. i9. i. 
gitur a Socrate illiid sentit ; Columna tangitur a 
Socrate ; Ergo Columna sentit. Vox sentit, non 
sponte, sed in hac structura est ambigua ; cujus 
vi, in Majori significat Sentit Socrates; in Con- 
clusione, Sentit Socraiem ; Quare Syllogismus 
habet quatuor terminos. 

3. 4. Fallacia Compositionis **, ubi datum in sensu Soph. 

^ Elench. 

4.6.20.1. 

c With the following account of the Fallacies may be com- 
pared the corresponding chapter in the Rhetoric, ii. 24. In 
doing so, however, it must be remembered, that the present 
sophisms occur in a disputation carried on in colloquial form 
between antagonists, and conforming to established rules ; 
whereas those are introduced ad lihitum, by an Orator in the 
course of his speech. Hence, though the principle of deception 
may be similar, the manner of its application will not always 
correspond. The same caution is still more necessary in 
examining modern specimens of Sophistry. 

^ This Fallacy, as treated by Aristotle, includes a wrong 
composition of clauses in a sentence capable of two punc- 
tuations. In this extension, the examples possible est se- 
dentem stare, dc. are easily included under Composition ; the 
sense varying according as sedentem is joined with possihile est, 
or with stare. The Fallacy of Division, in like manner, will 
include the separation of clauses which ought to be united. 



134 APPENDIX. 

diviso sumitur in sensu composito ; ut. Duo et Tria 
sunt Par et Impar ; Quinque sunt Duo et Tria ; 
Soph. Ergo Quinque sunt Par et Impar ^, Fallacia Divi- 
4. 7. 20. 1. sionis, quando datum in sensu composito sumitur 
in diviso ; ut, Planetce sunt septem : Sol et Luna 
sunt Planetce; Ergo Sol et Luna sunt septem. 
Utroque modo quatuor sunt termini si aperte 
loquaris. V. g. Prioris Syllogismi mens est. Duo 
et Tria seorsim accepta sunt Par et Impar. Quin- 
que sunt Duo et Tria in unum composita, &c. Poste- 
rioris vero, Planetse collective sumpti sunt sep- 
tem; Sol et Luna sunt Planetse distributive sumpti 
&c. Unde duplex utrobique Medius. 
Eien'h " ^\xc referri solent hujusmodi Orationes ; Pos- 

4. 6. 20. 4. <( sibile est album esse nigrum ; Possibile est seden- 
^* tem stare : dubito an satis recte ; quia tanto 
" acumine non est opus. Potest quidem album 
"fieri nigrum ; et Possibile est sedenti stare ; at 
" si haec velles, incongrue locutus es. Utraque 
" igitur Oratio est simpliciter neganda ; vel ut 
" aperte falsa si sit congrua, vel si non sit congrua, 
" quia non est Propositio." 
Eiench ^* Fallacia Accentus seu Prosodies^ potius, quando 

4. 8. 21* 1. 

e In these instances, the verbal defect lies in the copula. 
Two and three are (constitute) five. Two and three are 
(severally) even and odd. 

^ The Fallacia Prosodies, as Aristotle observes, is a Fallacy 
in writing only, not in speaking. Lepores and lepores have no 
ambiguity when rightly pronounced. The first example {servus 
ergo cervus), supposing the pronunciation of both words to be 
the same, is not properly an instance of this Fallacy. 



APPENDIX. 135 

pro eodem sumuntur quae vel Litera^ vel Spiritu, 

vel Tempore, vel Accentu sunt diversa : ut. Est 

servus Ergo est cervus; Est ara Ergo est hara. 

Est malum (an apple) Ergo malum (an evil). 

Venatur lepores Ergo et lepores; quibus qui falli 

potest, debet. 

6. Fallacia Figurce dictionis, quando propter Soph. 

dictiones similes, quod de uno datur de altero 4. 9. 22. i. 

arripitur : idque vel Grammatice^, ut Musa est 

8 Grammatice, i. e. inferring that Poeta is of the feminine 
gender, because the majority of words with the same termi- 
nation are so. Logice, inferring that videre belongs to the 
category oi iroulv, because most infinitive moods of this form 
are included under it. Thus viewed, it may be classed as in 
dictione, because the rules of gender and conjugation are dif- 
ferent in different languages. 

But the more common form in which this Fallacy would be 

stated is that of an induction, or rather a number of examples, 

after the manner of Socrates. Indeed, this very sophism is 

put into the mouth of Socrates by Aristophanes, Nubes, 

681 sqq. Stated in this form, the logical inconsequence is 

obvious ; as also if it is reduced to syllogism. " Such and 

such words are feminine; Musa resembles such and such 

words." Here there is no middle term. This ambiguity is 

sometimes called multiplex phantasticum. Cf. Petr. Hisp. 

Summ. Log. Tract, vi. " Est autem multiplex phantasticum, 

quando aliqaa dictio signihcat unum et videtur significare 

aliud, propter similitudinem quam habet in parte cum alia 

dictione : ut videre significat passionem, et videtur significare 

actionem, propter hoc quod est simile huic verbo, agere.'" In 

this form, it would seem more naturally to belong to the class 

extra dictionem. 

! In Ehefc. ii. 94. '2. Aristotle gives another form of this 

! Fallacy; viz. when a series of detached propositions are so 

I enunciated as to appear logically connected, not being really 

I so. See also Soph. Blench. 15. 5. 



136 APPENDIX. 

Foeminini generis. Ergo et Poeta: vel Logice, ut 
Docere est agere, Ergo et Videre, Haec Materia 
potius quam Forma peccat : et operose solvi non 
postulat : ponit aliquid aperte falsum ; quo negato 
evertitur. 



^^^''\ Fallaciae extra dictionem sunt septem^. 

Elench. ^ 

4. 10. 

Soph. §• "^^ ^' Fallacia Accidentis^ ; quando acciden- 

f^T^M 1 ^^^^^^^ aliquod confunditur cum eo quod est essen- 

tittle sen principaliter intentura : ut. Quod emisti 
Pol^;. J^^^-.M/comedisti, Crudum emisti; Ergo Crudum comedisti: 

in quo. Quod emisti, et Quale emisti, c,oiifuxi^\xiii\xr\ 

unde quatuor termini. 
Soph. 2. Fallacia a Dicto secundum Quid ad Dictum 

Elench. 

6. 2. 25. 1. Simpliciter ; quando proceditur a voce determinate 
sumpta, ad eandem absolute positam : ut, jEthiops 
est albus dentes ; Ergo albus: unde quatuor esse 
Terminos necesse est\ 



^ Fallacies extra dictionem embrace all those in which the 
deception arises from any other cause than ambiguity of 
language ; whether from a false assumption in the premise, 
or from the reasoning being unsound. Purely logical fallacies 
belong, not to the in dictione, but to the extra dictionem. 

i The example of this Fallacy given by Aristotle is, Coriscus 
is different from Socrates; Socrates is a man; therefore 
Coriscus is different from a man. The Fallacy lies in as- 
suming that whatever is different from a given subject is 
incompatible with all the predicates {ra o-vfi^aLvovTa) of that 
subject. The reasoning is thus illogical : Socrates is a man; 
Coriscus is not Socrates ; therefore Coriscus is not a man. 

^ The example as stated by Aristotle will run thus ; .^thiojps 



APPENDIX. 137 

[i 

3. Fallacia Isnorationis ElencJiL Elenchus^ Soph. 

^ . Elench. 

proprie Syllogismus est Adversarmm redarguens : 5. 5. 26. i. 
! confirmando scil. quod illius sententiae contradicat. 20. i. 
I Quare in banc incidit Fallaciam qui se putat Ad- E°ench. 
I versarium redargaere, non servatis Contradicendi 

Legibiis, (de quibus vide pag. 54.) Qui in bis 
I peccat, docendus est se nescire Quid sit Con- 
I tradicere. 
I 4. Fallacia a non-causa pro causa"^ ; sive sit a Soph. 

; ^ Elench. 

I 5.11.29.1. 

I non est alhus ; jEtliioys est alhus denies ; Ergo, qui est albus non ^^' ^^' H* 
est albus. Here there are four terms, and the Conchision, as 
Aristotle himself observes, is not drawn syllogistically. 

^ The Elenchus is defined by Aristotle, a-vWoyiafios dvri- 
4)d(T€(os, x\n. Pr. ii. 20. 1. Soph. Elench. 6. 4. The Ignoratio 
Elenchi consists in neglecting some of the conditions required 
by the rules of Dialectic for proving the contradictory of any 
given proposition. This is the case when the conclusion does 
not logically follow from the premises ; or when the premises 
themselves are not admitted by the opponent; or when the 
conclusion, though legitimately deduced from allowed pre- 
mises, is an apparent, not a real, contradiction of the op- 
ponent's position, failing in one of the four conditions of 
contradiction, viz. eodem modo, secundum idem, ad idem, eodem 
tempore. In this extended sense, every fallacy is an Ignoratio 
Elenchi, as is observed by Aristotle, Soph. Elench. 6. ] . though 
the name is especially applied to the last instance. 

™ This fallacy, according to Aristotle, most frequently occurs 
in the deductio ad impossibile, and consists in pretending that 
the proposition which we wish to refute is the cause of the 
false conclusion, which in reality follows from other premises; 
i. e. in maintaining that the conclusion is false because that 
particular assumption is false. This mode of deception has 
place in dialectical disputation, from the practice of asking 
the opponent to grant certain premises. An unnecessary 
proposition is asked and granted among the rest, and after- 



138 



APPENDIX. 



non-vera pro vera; sive a non-tali pro tali'': ut 
Cometa fulsit ; Ergo Belliim erit ; Nullo modo ; 
nam si fuerit^ aliis de Causis futurum est. Quod 
inebriat prohihendum est ; Vinum inehriat ; Nequa- 
quam vero, sed Abusus vini. Hxc Fallacia bene 
solvitur negando Causam falsam : melius, addu- 
cendo germanam. 

" Hue refertur ab aliquibus (qua de causa non 
" video) hoc Sophisma ; Qui magis esurit, plus 
" comedit ; Qui minus comedit, magis esurit ; Ergo 
'' Qui minus comedit, plus comedit, Sed qui hoc, 
" vel hujus simile attulerit (ut innumera afFerri 
" Solent) docendus est congrue loqui : Hoc si 
" fecerit, dicet in hoc casu. Qui magis esurit plus 
" comedet ; Qui minus comedit, magis esurit ; Ergo 
*' Qui minus comedit, plus comedet" 
Soph. 5. Fallacia Consequentis'', quando infertur quod 

Elench. 
5. 8.28. 1. 

wards selected as the false assumption. Aldrich's examples 
refer rather to the rhetorical than to the dialectical form of 
this fallacy. In this the speaker is guilty merely of a false 
assertion, attributing a certain effect to a wrong cause. See 
Ehet. ii. 24. 8. 

" In the non vera pro vera, there is no connexion between 
the effect and the supposed cause ; in the non tali pro tali, 
there is a connexion, but an insufl&cient one ; wine, e. g. does 
not intoxicate except in certain quantity. This instance, 
however, more properly belongs to the fallacy a dicta secundum 
quid ad dictum simpliciter, " Wine (in excess) intoxicates ; 
therefore. Wine (absolutely) is to be forbidden." 

^ The fallacia consequencis is an error in reasoning, as may 
be clearly seen in the examples given Soph. Elench. 5. 8. and 
Rhet. ii. 24. 7. e. g. Honey is yellow ; Gall is yellow ; there- 



APPENDIX. 139 

non sequitur : ut. Animal est ; Ergo, Est Homo, 
Hie memineris, quod si recte ratione uti volumus, 
Consequentia aut directa, immediata, formalis, aut 
plane nulla est ; peccat enim contra aliquam Dia- 
lecticae regulam ; ad quam si provoces, refelletur. 

6. Fallacia Petitionis Principii^, cum ut datum Soph. 

. Elench. 

assumitur, quod probatum oportuit. V. g. Cum 5. 7. 27. 1. 

, T • 1 1 • -r Anal. Pr. 

probatur aliquid vei per seipsum, (quae vocatur 11. 16. 1. 
Petitio statim,) ut. Homo est, Ergo, est Homo : isl^i. 
Vel per Synonymum ; ut Ensis est acutus ; Ergo, 
Gladius : Vel per aeque ignotum ; ut Hie est Pater 
Melchisedek ; Ergo, Hcec Mater: Vel per ignotius ; 
ut, Hoc Quadratiim est kujus Trianguli duplum, 
Quia huic Circulo cequale : Vel per Circulum ; re- 
sumendo scilicet quod relictum est ; ut si diceres. 
Ignis est calidus, Ergo urit : et post pauca. Ignis 
urit, Ergo est calidus, 

7. Fallacia "^ plurium interrogationum, quando Soph. 
plures quaestiones velut una proponuntur ; v. g. 5.13.36.1. 
Suntne Mel et Pel dulcia f Estne homo animal et 

fore gall is honey. Here the middle term is undistributed. 
Another specimen cited by Aristotle is the reasoning of 
Melissus; "Whatever is generated has a beginning; the 
universe is not generated ; therefore it has not a beginning." 
Cf. Phys. Ausc. I. 3. 2. Here there is an illicit process of the 
major term. 

p On the 'Petitio Principii, see Appendix, note E. Aristotle 
enumerates five varieties : which, however, are not the same 
as those given by Aldrich. See Top. viii. 13. 

q This is merely a dialectical fallacy; and consists in 
entrapping an opponent into an answer partly false, by 
artfully putting two questions as one. 



140 APPENDIX. 

lapis? Evertitui% ad singulas quaestiones distincte 
respondendo ; sicut fecit Menedemus Eretriensis, 
qui rogante eum Alexin o, Numquid Pair em ver- 
her are desiisset ? Nee verheravi, inquit, nee desii\ 

Atque hae sunt tredecim Sophismatum formulae^ 
Veteribus usitatiores, quae Tironibus Logicis in 
exemplum proponi solent. Poterant esse pauci- 
ores ; nam videntur aliquae coincidere ; et prae- 
terea tres, Non-causa pro Causa, Petitio Principii, 
et Plures interrogationes, non sunt Fallaciae proprie 
dictae, h. e. Syllogismi Forma peccantes* ; sed Vitia 
male Opponentis. Poterant et plures ""; sed cum 
hie numerus Aristoteli satisfecisset, idem omnibus 
post ilium Logicis satisfecit. 

§. 5. SoPHisMATiBus ex sententia veterum accen- 

' Diog. Laert. ii. 135. 

s These thirteen fallacies are comprised in the mnemonic 
lines, 

iEquivocat, Amphi. Componit, Dividit, Ace. Fi. 
Acci. Quid, Ignorans, Non causa, Con. Petit. Interr. 
* Aristotle's definition of Fallacy will include logical de- 
ductions from false premises, as well as illogical deductions 
from any premises. See Top. i. 1. 3. 'EpiariKos S' eVri avX- 

Xoyiaixos 6 €k (fjaivoixevcov ivho^cov, firj oirra>v Be, Koi 6 e| iubo^cov fj 

^aivofjievav evdo^av (f)aiv6fievos. Aldrich's limitation to Syllogisms 
faulty in form is quite arbitrary. 

" Aristotle does not profess to give a complete enumeration 
of the fallacies ; but only a list of such as may be solved 
by the Dialectician. There may be innumerable false as- 
sumptions, on matters not belonging to Dialectic, which must 
be refuted from the principles of the Science or Art to which 
they belong. See Soph. Elench. 9. 1 . 



I 



APPENDIX. 141 

sendae sunt Inexplicabiles (ut vocantur) Rationes, 
quas Megarici, Stoici, aliique Eristicam professi, 
propriis nominibus insignivere, Crocodilus, Mentiens, 
Ohvelatus, &c. quas plerasque collegit Gassendus, 
et retulit in Libido de Origine et Varietate Logicce : 
Nos eodem fere ordine explorabimus quo ab illo 
sunt propositae. 

1. Achilles vocatur Argumentum quo usus est Arist.Phys. 

Ausc. VI. 

Zeno Lleates, non ut Motum tolleret, quod vulffo o. 3. 

1 P 1 T . 1 1 r^ • Top. VIII. 

sed lalso dicitur ; sed ut ostenderet Continuum 8. 2. 
non esse infinite divisibile^ quia hoc dato Motus E°ench. 

24 5 

toUeretur. Argumentum sic se habet. Sit Achilles 
quantum voles woda^ a^Kv^, puta decuplo velocior 
Testudine. Quiescente illo, confccerit Testudo 
partem aliquam (puta decimam) spatii percurrendi. 
Tum procedat Achilles, idemque spatium per- 
currat : progredietur interim Testudo per partem 
ejus decimam, h. e. totius spatii centesimam ; banc 
conficiat Achilles, et percurret interim Testudo 
hujus centesimae decimam ; et sic deinceps in 
infinitum ; quo fiet ut Achilles nunquam asse- 
quatur Testudinem\ 

^ We must not confound the metaphysical difficulties con- 
nected with the infinite divisibility of space, with the logical 
difficulty of a false conclusion apparently deduced from true 
premises. Archbishop Whately evades the latter, by ob- 
serving, that the sophism cannot be exhibited in a Syllogism. 
But this confession is in fact a surrender of the syllogistic 
criterion, as a means of discriminating between sound and 
unsound reasoning. On the contrary, nothing is easier than 
to exhibit the reasoning in a Syllogism, and to shew thereby 



142 APPENDIX. 



Ineptum est hoc Sophisma. 1. Quia solvitur 
ambulando; quod fecit Diogenes ^ 2. Quoniam 
ex ipsa Hypothesi, Dum Testudo quae praecessit 
spatio A, conficit ^ A, Achilles conficiet 2 A; 



that the fallacy does not lie in the form, but in the matter. 
Thus, representing the whole space to be traversed by a, 

" Any space equal to ^ + ^^^ + j^^ &c. is infinite, (being 
the sum of an infinite series.) The space to be passed before 
Achilles overtakes the tortoise is equal to this sum. There- 
fore it is infinite." 

The whole logical mystery of this famous fallacy lies in 
this, that the major premise is false. The sum of an infinite 
series may be, and in this case is, finite. This premise is 
equally false, whether space is or is not divisible ad infinitum. 
On the metaphysical question connected with the matter of 
the sophism, see Hegel, Werke, vol. iii. p. 218. Fries, System 
der Logik, §. 109. Herbart, Einleitung in die Philosophie, §. 139. 
Trendelenburg, Logische Untersuchwigen, vol. i. p. 179. The 
solution attempted by Coleridge, {Friend, vol. iii. p. 93.) is 
refated by Herbart. 

It may be observed, that Aldrich is mistaken as regards 
Zeno's object in this Sophism. It was proposed to support 
the leading tenet of Parmenides, of the unity of all things, by 
shewing that the identity of rest and motion is a necessary 
result from the contrary opinion. It does not appear, however, 
that Zeno advanced this argument seriously. His principal 
design was to retort the ridicule which had been thrown on 
the doctrine of Parmenides, by involving his opponents in 
the same absurdities which they professed to find in his 
theory. Cf. Plato, Farm. p. 1-28. Arist. Soph. Elench. 10. 2. 
38. 4. Cousin. Nouveaux Fragments, Zenon dFlee. 

y The solution of Diogenes proves nothing. Zeno contends 
that reason contradicts the evidence of the senses. Diogenes 
replies that the evidence of the senses contradicts that of 
reason. Who denied that? 



APPENDIX. 143 

adeoque statim assequetur earn, et antecedet^ 
Sed hoc (inquies) in casu proposito nunquam fiet; 
Recte ; Ne enim fiat, in ipso proponendi modo 
clam inseritur nova conditio. Nam 3. Argumen- 
tum aliis verbis hoc dicit ; Si Achillem decuplo 
velociorem praecesserit Testudo ; et uterque meo 
pergat arhitratu ; Ego perficiam ne Achilles asse- 
quatur Testudinem: Quare prorsus nunquam asse- 
quetur. Quae est Fallacia a dicto secundum quid, 
ad dictum simpliciter. 

2. Diodorus Cronus, quod Sophismata Stilponis 
non solvisset, exinde ovos appellatus est*; id cog- 
nominis aliunde promeritus, quod ad hunc modum 
contra Motum disputaret. Mobile movetur vel in 
quo est loco, vel in quo non est ; At neutrum horum; 
Ergo No7i omnino, Unde facete ilium lusit Hero- 
philus, qui ut luxatum illi humerum restitueret 
rogatus, Tuus (in quit) humerus vel in quo erat loco 

^ The futility of this attempt at solution might have been 
learned from Aristotle, Soph. Elench. 24. 5. It only shews 
that the contradictory assertion rests also on seemingly valid 
reasoning ; whereas the duty of the opponent is to shew 
where the fallacy of Zeno's reasoning lies. 

* The facetious Iambics in which Diodorus was thus " writ 
down an ass "' are as follows : 

Kpoi/e AtoScope, t'is ae dai^ovcov KaKrj 

"lu avTos avTov iix^akrjs els rdprapov, 

^TikTTcovos ov \vcras €7rr] 
Aluiyixarcibr] ; roiyap cvpedrjs Kpovos 
"E^a> ye tov poi Kamra re. 

See Diog. Laert. ii. 1 1 2. 



144 APPENDIX. 

existens excidit, vel in quo non erat. Sed neutrum 
horum ; Ergo non omnino. Diodori argumento 
breviter et perspicue respondet Gassendus, Quod 
movetur moveri a loco in quo erat^ per locum in 
quo est (sive quern pertransit), ad locum in quo 
nondum est^ sed futurum est^ 

3. Reciprocum vocat Argumentum Gellius, quod 
Graece dicitur ' AvTicrrpe^ov: cui illustrando con- 
ficta est Fabula quae Grascorum vanitatem olet. 
Narrant enim inter Protagorum et Euathlum, vel 
(ut facetiae locus sit) inter Coracem'' et Tisiam 
convenisse, ut hunc ille Dialecticam doceret ; 
idque hac lege, ut diraidium mercedis statim ac- 
ciperet ; reliquum, cum discipulus causam vicisset. 

^ The true solution of the sophism of Diodorus is, that the 
disjunctive premise is false. " The place where a body is," 
is contradictory of "the place where a body is not;" as 
"Englishmen" is contradictory of " not-Englishmen ;" but 
** moving in the place where it is," is no more contradictory 
of" moving in the place where it is not," than " an army com- 
posed of Englishmen " is contradictory of " an army composed 
of not-Englishmen." As it would be false to say, " every army 
must be composed of Englishmen or not-Englishmen," to the 
exclusion of the third possibility of a mixed force, so it is \ 
false to say, " Every body must move in the place where it 
is, or in the place where it is not," to the exclusion of the 
third possibility of moving partly in the one and partly in 
the other. This solution is substantially given by Hobbes, I 
Philosophia Prima, P. 11. c. 8. §. 11. 

^ The story is told of Protagoras and Euathlus by Aulus 
Gellius, V. 10. and by Apuleius, Florid, iv. 18.; of Corax, by (• 
Sext. Empir. adv. Math. p. 81. Cf. Menag. ad Diog. Laert. 
ix. 56. 



APPENDIX. 145 

Primam exinde litem cum Discipulo contestatus 
est Magister, cum mercedis reliquum lege peteret ; 
apud Judices vero sic agebat : Ego si vicero, Tisia, 
Tu solves ex sententia, sin minus, ex pacto ; utroque 
igitur modo solvendum est, Respondit Tisias^ Ego 
nihil solvo ; Tu si viceris, ex pacto ; sin minus, ex 
sententia, Tanto utrinque acumine perculsi boni 
judices, exclamarunt Ka/coi) Kopa/cos" KaKov coov^ 
causamque in longissimum diem distulerunt. 

Ineptum erat Coracis Dilemma quia potuit tarn 
bane retorqueri. Nihilominus callide agebat, si id 
Judices vidissent. Nam cum mercedem iniqua 
peteret, causa cadere debebat ; Quamprimum autem 
cecidisset, ei merces ex pacto debebatur, 

§. 6. 4. Mentiens quae est Graece ^evdofxepos^, Soph. 
Chrysippi Syllogismus ne ab ipso quidem solutus, 25. 3. 
praeter caeteros insolubilis habetur. Eum Cicero^ vii.' 3.^8. 
sic enuntiat : Si dicis Te mentiri, et verum dicis, men- 
tiris ; Sed dicis Te mentiri, et verum dicis ; mentiris 
'gitur, 

Congrue loquere, Chrysippe, et intelliges Te vel 
nihil prorsus, vel nihil dicere difficile. Qui se dicit 

^ This Fallacy is attributed to Eubulides of Miletus. See 
Laert. ii. 138. It is mentioned by Aristotle, Eth. Nic. vii. 
3. 8. and consequently must be older than Chrysippus. 

' Acad. Quaest. iv. 30. Its solution i& obvious. No one can 
jlie without lying about something. The something is not stated 
in the sophism. The questicm as it stands is unmeaning. Is 
ithis thing very like ? Like what ? 
i 

L 



146 APPENDIX. 

mentitumi et verum dicit, mentitiis est ; Qui menti- 
turum, mentietur, Horum utrumque verum est, et 
nemini obscurum. Sed qui ut verum simul dicat 
et mentiatur dicit unum aliquid, cujus partes sibi 
invicem contradicunt, is nee verum, nee falsum, 
sed omnino nihil dicit : quando enim sentential 
pars una evertit alteram, tota nihil prorsus signi- 
ficat, sed inaniter strepit. 

Subtilius disputare videbantur qui sic agebant. 
Cretenses esse mendaces dicit Epimenides Cretensis, 
Mentitur igitiir ; Ergo Illi sunt veraces ; Ergo et 
Ille verum dicit ; Ergo Illi rursus sunt mendaces &c, 
Sed profecto nihil stultius est hoc Argumento, nisi 
vox Cretenses eos ad unum omnes significet, et 
Ornnis mendax quicquid dicit mentiatur ^ 

Videtur hie Mentiens peperisse subtilem illam 
Scholasticorum de Insoluhilihus doctrinam. " Nam 
" talia argumenta (inquit Occarn) non possunt fieri 
" nisi quando actus humanus respicit istum termi- 
" num Falsum, vel aliquem consimilem affirmative; 
" vel hunc terminum Verum, vel ahquem consimilem ( 
"negative^." Esse haec Sophismata ante dixerat; 
nee vocari Insoluhilia, " quia nuUo modo solvi 
*' possunt, sed quia cum difficultate solvuntur." 

Insolubilis exemplum sic proponitur. Incipiatj, 

Socrates sic loqui, Socrates dicit falsum ; et nihil 

■■) 
f This Fallacy is solved by Fries, §. 109. A man who isit 
always a liar cannot possibly say or imply " I lie ;" for this 
would be a truth, and thus he would not be always a liar. 
« Occam, Logica, iii. 3. cap. 45. 



I APPENDIX. 147 

amplius loquatur : turn interroget aliquis, utrum 

I vera an falsa sit haec propositi o. Respondeo, nee 

jveram nee falsam esse, sed nihil significare, nisi 

aliquid aliud respiciat, quod a Socrate ante dictum 

j supponitur. Qui enim profert haec verba, Socrates 

I dicit /ahum, fert judicium de dicto Socratis ; qui- 

que fert judicium, necessario prsesupponit aliquid 

de quo judicet : Unde cum sententia praesupponat 

objectum suum, clarum est eandem numero pro- 

positionem, et sententiam et ejus objectum esse 

non posse. Quare et Scholarum subtilitas hie nihil 

proficit ; nihilque opus est plura dicere de Insolu- 

bilibus. 

5. Fallens /^LoKavOdvcov^, vel ut alii AiaXeXrjOcoy, 
de Juramento ludit sicut Mentiens de nuda affirma- 
tione. E. g. Qui jurat se falsum jurare et falsum 
jurat, vere jurat. Quare eodem fere modo quo 
Mentiens explicatur. 

§. 7. 6. 7. Obvelatus, alio nomine Electra, est Soph. 
Fallacia a dicto secundum Quid ad dictum Simpli- 24. 2. 
citer. Nam colligere pertendit, quod et Patrem 

Filius et Soror Fratrem, h. e. Electra Orestem 

I 

^prorsus nesciat, si eundem velo obductum se nescire 
! fateatur'. 



^ The AiaXaj/^ai/wi; is properly a similar Fallacy to the Electra 
j and the Obvelatus. The honour of its invention is divided 
' between Eubulides and Diodorus Cronus. The example 
I given by Aldrich is a mere conjecture of Gassendi's. 
I ^ The Fallacy of the Electra is founded on Sophocles, 

I l2 



148 APPENDIX. 

8. 9. AcERVALis et Calvus'', sunt ejusdem Sophis- 
matis duo tantum Exempla. V. g. Si rogatus a 
Sophista, neges te Calvum fieri amisso crine uno, 
duobus, tribus, et sic deinceps ad 99, sed amissis 
centum concedas; vel eodem modo neges 99 grana 
Acervum esse, centum autem esse fatearis ; con- 
cludet ille grano unico adjecto Acervum fieri ; 
crine unico amisso, Calvitiem. Facile autem re- 
spondetur, Unum centesimum non esse Unicum ; 
nam est Unum cum nonaginta novem. Vel si 
mavis sic ; Fit Acervus, grano uno, sed adjecto ; 
adeoque non unico, sed cum pluribus aliis. Fit 
Calvities crine uno, sed post multos alios, amisso. 

10. CoRNUTUS et Ceratinus, Ceratine, Ceratis, et 
Ceras dicitur Sophisma illud ante memoratum. 



Elect. 1222. It is given as follows by Lucian, Vit. Auct. 
§. 22. irapearTaTOs yap avrfj tov ^Opecrrov en dypa>Tos, oide fxep 
*Op€(rTr)Vy OTi ddeXcf)6s aires' ort Se ovtos 'OpecrrT/y, dyvoel. The 
Obvelatus is of similar character. XPY2. "Uu o-oi, Trapacrnjo-as 
Tiva €yK€Ka\vp.p€vov, epcopai, tovtov olxrOa ; Ti (fyrjaeis ; AFC. ArjXad^ 
dyvoeiv, XPY2. 'AXXa /xeV avrbs ovtos rjv 6 Trarrjp 6 cros, ajcrre et tovtov 
dyvoels, di]Xos el tov Trarepa tov crbv dyvoav. Another variety of the 

same sophism will be found in Aristotle, Soph. Elench. 24. 2. 
where it is classed under the Fallacia Accidentis. Diogenes 
Laertius, ii. §. 108. attributes the Electra and Obvelatus to 
Eubulides, as well as the Acei'vus, Cornutus, and Calvits. 

^ These two Fallacies, which are in fact but one under 
different names, are alkided to by Horace, Ep. ii. 1. 45. and 
by Persius, Sat. vi. 80. The Acervus is frequently called 
Sorites, (cf. Cic. Acad. Qutsst. iv. 49. De Divin. ii. 11.) but 
must not be confounded with the series of syllogisms of the 
same name. 



I 



APPENDIX. 149 

' Quod non amisisti habes &c. Quae est Petitio 
\ Principii ; nam supponit Te cornua habuisse. 
; Ineptissima haec Fallacia plus acuminis praefert 
ijuxta veterem Disputandi modum rogando pro- 
iposita* Erit enim fortasse, qui rogatus. Quod non 

amiserit, utrum habeat necne? non intelligat se 
jcaptum iri, si simpliciter respondeat; sive habere 
jse, sive non habere dicat. Nam eum adiget 
'Sophista, ut vel se habere Cornua^ vel non habere 
j Oculos fateatur. 
i 11. Acutus sibi videbatur Menedemus (Eretri- 

ensis scil. quem epLaTiKcoTaTov appellat Laertius) 
iquum ad hunc modum nugaretur. Diversum, a 
\Dwerso Diversum est; Prodesse est a Bono Di- 
\versum; Prodesse igitur non est Bonum\ Quae 
lest crassa et putida ^quivocatio ; et nihil am- 
plius. 

§. 8. 12. Crocodilus"" a Chrysippo inventus, qui 
ad Fallaciam Consequentis revocari poterit, sic 
proponitur. Surripuerat infantem Crocodilus ; red- 
diturum se, hac lege pollicitus, ut divinet mater, 
utrum apud se reddere an non reddere constituent. 
Si dicat mater Non reddere ; mentietur si infantem 
receperit : Si dicat reddere ; non reddet quia hoc 
est falsum. Quamobrem Chrysippus nihil esse 
putat difficilius quam responsum matri suggerere. 

I i Diog. Laert. ii. 134. 

I ™ This Fallacy is given at length by Lucian, Vit. i^uct. §. 22. 



150 APPENDIX. 

Nec injuria, si lubricum putet divinare ; sed im- 
merito, si in hoc (ut videtur) hsereat. Quod si 
puerum Crocodilus non reddere constituent, 
quamvis id Mater divinaverit non reddet: quasi 
consilium quod primum intenderat Crocodilus, 
postquam indicatum est, repudiare non possit, et 
ex pacto non debeat : nam si Mater recte divina- 
verit, recepto puero, non mentitur ilia, sed consi- 
lium mutat Crocodilus. 

13. Metens Gepi^cov qui vocatur, ita placuit 
Zenoni Stoico, ut Sophistae a quo eum didicerat 
duplum pactae mercedis numerat. Proponente 
Ammonio"" sic se habet. Si messurus es, nonfortasse 
metes, foriasse non metes, sed metes omnino ; Pariter, 
si non messurus es, non fortasse metes, fortasse non 
metes, sed prorsus non metes. Atqui vel metere te, 
vel non metere, necessarium est; perit igitur For- 
tasse, quod in neutra hypotJiesi locum habet, Fortu- 
natum Sophistam ! qui mercede dupla hunc fumum 
vendidit ; Vel hoc, vel illud evenire est necesse ; 
Quare hoc et non illud necessario eventurum est. 
Nihil amplius dicit qui sic dixerit, Ut vel metas 
vel non metas est necesse: Ergo Vel necessario metes\ 
vel necessario non metes, Breviter, haec Fallacia] 
Divisionis est ; nam in Antecedente, Modus Neces- 
sario, non tribuitur nisi toti Disjunctivae ; sed inj 
Consequente dicitur de ejusdem membris seorsimj 
acceptis. 

" In de Interp. sect. 2. cap. 10. cf. Menage ad Laert. vii. 25. 



APPENDIX. 151 

14. Ignava Ratio vel *Apyo9 X6yo9 appellatur% 
qui si valeat nihil est omnino quod agamus in vita. 
V. g. Si Fatum est cegroto convalescere, sive medicum 
adhihuerlt sive non adhibuerit, convalescet : Pariter, 
si illi Fatum est non convalescere, sive medicum 
adhibuerit, sive non adhibuerit, non convalescet: et 
alterutrum Fatum est; medicum ergo adhibere nihil 
attinet, Lepide respondit Chrysippus posse esse 
Confatalia adhibere medicum et convalescere : 
Quemadmodum et Zeno^ quando servum furem 
verberabat, Furari sibi Fatum esse dicenti, et 
Vapulare respondit. Sed commodius dici vide- 
tur. Si sit Fatum, hoc valere argumentum ; idque 
vel solum sufficere ne Fatum esse concedamus. 
Argumentum hocce et quae praecedunt pp. 143, 
144. N°. 2. et 3. ex Dilemmatis legibus facile 
solvuntur. 

§. 9. Plura sunt apud Autores Inexplicabilium 
Rationum nomina ; quorum exempla Gassendus 
quia nusquam invenisset, ipse reperit. Verum ea 
relinquimus studiosis ; quibus etiam consulto est 
relictum, ut quae sunt hactenus explicata, illi 
explicent in Syllogismos conversa. Exempla Gas- 
sendi ne desiderent qui libro carent, non pigebit 
exscribere. 

Dominans, Kvpcevcou, Themistoclis filius nee 
Graecis imperat, nee de imperando cogitat : Verum 
imperat Matri, quae imperat Themistocli, qui 

» See Cicero, de Facto, c. 12. 



152 APPENDIX. 

Grsecis imperat ; Dominatur itaque Grsecis, et non- 
dominatur^ , 

Conficiens, Ylepali/cop, Multum itineris corificit, 
et non conficit Canis, qui in rota gradiens totum 
diem, ex eodem tamen loco non recedit. 

Superpositus vel Superlativus, 'YTrepOerLKo^, Soriti 
forte affinis ; Ut si roges quota sit palea, quae si 
mulo super-imponatur ille oneri succumbat ? 
Soph. Nullus^ OvTL9* HoHio in Communi nee est hie, 

Elench. 

22.12. nec ille, nee alius homo singularis. Ergo Nulhis\ 
Vel ut tritum Sophisma : Quod Ego sum, Tu non 
es ; Ego sum homo : Ergo Tu non es. Vel denique 
ut Chrysippus. Qui est Megaris, non est Athenis ; 
Homo est Megaris ; Ergo Homo non est Athenis^, 

P The Fallacy Kupievcoi/ is mentioned by several writers, but 
not explained by any. Cf. AiTian, Epicteti Dissert, ii. 1^. 
Lucian, Vit. Auct. c. 22. Plutarch, Sympos. I. i. 5. Gellius, 
Noct. Att. I. 2. It probably derived its name rather from its 
supposed dignity as an argument than, as Gassendi con- 
jectures, from the mention of a ruler. The same may be said 
of the liepalvoiv or conclusive sophism. 

^ This sometimes appears in another form, as one of the 
various expositions of the celebrated Fallacy of the tertius 
homo, alluded to by Aristotle, Soph. Elench. 22. 12. Metaph. 
i. 9. 3. It is given by Alexander, Schol. p. 314. b. 42. In 
the proposition, dvdpatTros nepiTraTel, the subject is not the Pla- 
tonic avTodvdpcoTTos, who is immoveable, nor yet any individual 
man ; therefore there is a third man, distinct from the Idea 
and from the individuals. Several other forms of this Fallacy 
are given by Alex, in Metaph. p. 62. ed. Bonitz. Cf. Brandis, 
de perditis Aristotelis libris, p. 18. Cousin, de la Metaphysiqice 
d'Aristote, p. 164. Bonitz in Aiist. Met. 990. b. 15. 

' Ajnmonius ad Categ. Arist. f. 58. ol OvriBes 7rapdKoyicrp.o\ 
Kara tqv irap 'Op,r}pa} '08v(r(rea, ep Kaipa Ovtiv iavrov KoKeaavra. 



APPENDIX. 153 

Subjicit Gassendus ex Laertio, has Chrysippi 
Rogatiunculas. 1. Qui non initiatis indicat mys- 

'teria, impie agit. Sed hoc facit Hierophantes ; 

I Ergo Impie agit. 2. Est quoddam caput ; Id Tu 

j non habes ; Ergo Caput non habes. 3. Id quod 
loqueris ex ore tuo egreditur : Currum loqueris ; 

[Ergo Currus ex ore tuo egreditur. 



§. 10. Non temperaturos sibi Juvenes satis scio 
quin dissihant risu, ubi hsec tarn futiHa intellexerint 
a gravissimis Philosophis serio fuisse proposita ; et 
Veteribus adeo difficiha haberi, ut Philetas Cous 
praeceptor Ptolemaei Philadelphi soHus Mentientis 
explicandi studio confectus interierit. Quamvis 
autem Aristotehs beneficio^ videantur ista ut sunt 
llevia, in iis tamen prompte atque artificiose sol- 
vendis non inutihter sese Juvenes exercebunt : 
nam in gravissimis Disputationibus, haec eadem 
recocta Novae prsesertim Philosophise cultores 
saepissime reponunt. 

V. g. Gassendus Vacuum quod appellat disse- 
minatum eodem fere Sophismate demonstrare per- 
tendit, quo olim Zeno contra motum utebatur : 
Suamque Hohhius de Necessitate sententiam iisdem 
propugnat Fallaciis quibus Fatum Stoici : ahaque 
plurima hujus generis, quae sunt Nobis praetereunda, 
studiosis inter legendum occurrent. 

OijTivos TrapaXoyiafxoi) napad^Ly^a. Ei ris iuTLV iv 'Adrjvais, ovtos ovk 
ea-Tiv iv Meydpois' av6pa>iros 5e ioTiv iv 'Adrjvms' av6pa>iros apa ovk 
€<mv iv Meydpois. 



154 APPENDIX. 

Fefellit Virum satis alias perspicacem hsec se- 
quela^ quae in Ambiguis distinguendis versatum 
minime (opinor) fefellisset ; Possum datce peri- 
pherice trientem exhihere^ ; Possum igitur datam 
peripheriam trisecare : cujus falsitatem ipsa Praxis 
redarguit ; neque enim trientem exhibuit, sed 
alterius circuli peripheriam trienti parem : h. e. 
non trientem ipsum^ sed trientis valorem : Paria 
fecisset qui oblatum sibi solidum trisecturus^ ne 
attrectato quidem solido porrexisset drachmam^ 

§.11. VoLENTEM hie desiuere pungit scrupulus, 
qui nonnullos hodie Mathematicos male habet. 
Nam in Demonstrationibus quibusdam^ Conclu- 
sionem ex sui Contradictoria, per legitimas neces- 
sariasque consequentias directe inferri volunt. 
Quod si ita sit^ miror a Veteribus, praesertim 
Scepticis non fuisse animadversum ; quippe hoc 
dato tota ruat Logica necesse est. 

Dicunt tamen Theodosium demonstrasse quod 
si Maris superficies non est Sphcerica, est Sphcerica. 

s DatcB 'peripherice trientem. Aldrich appears to have mis- 
taken the problem. There is no difficulty in trisecting the 
entire circumference of a circle, which may be done by in- 
scribing an equilateral triangle, (Euclid iv. 2.) The tnie 
problem is to trisect an angle, or the arc subtending a given 
angle. The solution to which Aldrich alludes appears to 
have been of this kind. If an arc be drawn subtending a 
given angle with a radius = a, and another with a radius 
■=: J a, the latter arc = ^ of the former. But the larger arc 
is not thereby trisected. For the materials of this note I am 
indebted to Professor De Morgan. 



APPENDIX. 155 

Verum ille nihil tale demonstravit ; sed tantum 
Maris superficiem si nondum esset,fore Sphcericam: 
siquid enim emineat (inquit) illud statim^ ex natura 
humidi, subsidet : Unde si Maris superficies sit (ut 
non est) inaequalis,^^^ perfecte Sphaerica. 

Videamus aliud Exemplum. Sunto numeri duo 
inaequales, et inter se primi ; Dico quod eorum 
differentia ad minorem prima est. Esto enim 
numerus aliquis qui metitur minorem; idemque 
metiatur difFerentiam : Ergo metitur eorum sum- 
mam; Ergo metitur majorem, huic summae parem; 
Ergo non metitur minorem. 

Possum hoc loco dicere quod mendose colligitur; 
siquis enim numerus minorem metiatur ex sup- 
posito, et majorem ex demonstrato ; colligendum 
erat datos esse inter se compositos, quod est contra 
Hypothesin, Verum ne pluribus exemplis sim 
molestus, malo generale responsum. Dico igitur. 
Quod nulla hujusmodi Demonstratio supponit 
solam suae Conclusionis Contradictoriam ; sed quae- 
libet cum Contradictoria ponit aliquid quod eam 
evertit ; et evertere, demonstrando ostendit. Quare 
Conclusionem non infert ex ejus Contradictoria; 
sed ex Contradictoria cum Contradictoriae ever- 
siva : quod si faciat nihil mirum. Nam Si Socrates 
V. g. est homo, et irraiionalis, tum Si est homo, non 
est homo : Et Si Socrates est mortuus, et scit se esse 
mortuum, tum Si est mortuus non est mortuus: 
Et Universaliter, Si et hcec est vera et quce hanc 
evertit: tum Si hcec est vera, non est vera: quibus 



156 APPENDIX. 

omnibus inest una quae est prorsus nulla diffi- 
cultas. Ubi enim Hypothesis evertit suppo- 
sitionem, quidni ex Hypothesi sequatur, quod 
Suppositioni contradicit ? 



APPENDIX 



A. On the Predicables. 

B. On the Categories. 

C. On Definition. 

D. On Material and Formal Consequence. 

E. Is THE Syllogism a Petitio Principii ? 

F. On the Enthymeme. 

G. On Induction. 

H. On Example and Analogy. 

I. On THE Hypothetical Syllogism. 

K. On THE Demonstrative Syllogism. 

L. On the Logic of Geometry. 

M. On the Classification of Fallacies. 



APPENDIX 



Note A. 

ON THE PREDICABLES. 

It has been already observed that the ordinary 
logical account of the Predicables, even in its least 
objectionable form, as it occurs in the Isagoge of Por- 
phyry, cannot be consistently maintained, except upon 
Realist principles. By this is meant, that there are 
portions of that account altogether untenable, except on 
the supposition that Genera and Species are not mere 
conceptions of the human mind, but have an independent 
existence in Nature. Whether they are to be regarded 
as existing separately, as in the Platonic theory of ideas, 
or in the individuals, according to the view sometimes 
attributed to Aristotle, (for both these opinions had their 
advocates among the Schoolmen*,) is in this respect 
immaterial ; though it may be observed by the way, that 
of the various modifications to which Realism has at 
different times been subjected, the Platonic hypothesis 
is by far the most consistent and intelligible. The 

* Both were early, almost simultaneous, developments of the scholastic 
Realism, appearing as soon as the Nominalism of Roscelin compelled the 
antagonist doctrines to assume a definite form. The Platonic theory was 
advocated by Bernard of Chartres ; the other, ultimately the prevailing 
doctrine, found its earliest scholastic supporter in William of Champeaux. 



160 APPENDIX. 

points which may be considered as especially demanding 
the Realist hypothesis are, 

1. The admission, under any definition, of an Injima 
Species, 

2. The definition frequently adopted of such Species, 
as being the whole essence of the individuals of which it 
is predicated. 

3. The assumption that every such Species has one 
absolute differentia, convertible with the Species, and 

I serving to distinguish it from every other. 

It is not asserted that these views were held by none 
but professed Realists. The first, indeed, may be traced 
to Aristotle, who has by different writers been regarded 
as a Realist, a Conceptualist, and a Nominalist, in the 
strictest sense ^; it is also to be found in Porphyry, who 
in the commencement of his treatise proclaims himself 
neutral; and it was subsequently adopted by the scholastic 
Nominalists ^ The second is held by Boethius, who, as 
far as he had any definite views, rather inclines to Con- 
ceptualism ^ ; and the third, though not formally established 
in the schools till the time of Aquinas, was afterwards 
adopted by Nominalists and Realists indifferently^. But 
this does not prove the compatibility of the doctrines, 
but only the inconsistency of their holders. The Realist, 
when pressed to declare why he has fixed the Injima 

b See Hamilton on Reid, p. 405. 

« Abelard, ed. Cousin, p. 537. Occam, Logic, pt. i. chap. 21. 

^ Boethii Opera, p. 72. 

« The Porphyrian definition of man, " Animal rationale mortale," wa& 
adopted by the earlier Schoolmen, Abelard, Albertus Magnus, and Petrus 
Hispanus ; though sometimes with the sa-sing clause, that it must be 
understood with reference to the Stoical notions of the Gods, Aquinas 
was the first who expelled the Genus animal rationale from the Arbor 
Porphyriana, and, limiting rationality to men, distinguished Angels as 
intellectuales. Cf. Summa, P. i. Qu. Iviii. 3. Opusc. xlviii. Tract. 1. cap. 4. 
Tract. 2. cap. 3. ^ 



APPENDIX. WX 

Sfjecies at Homo, has an obvious and sufficient answer. 
I did not make the world, he might say. Substances, 
universal as well as singular, exist independently of 
me : I state facts as I find them, and am not bound to 
determine why they are so. But let a Conceptualist or 
Nominalist^ talk of a Lowest Species, and he is refuted 
at once by his own fundamental doctrine. The several 
Species are our own creation, as abstract ideas, or as 
significations of w^ords. You have no right arbitrarily 
to declare that you will form complex conceptions thus 
low and no lower ; or, at least, if you fix such limits for 
your own convenience, you have no right to impose the 
same restriction on others. 

The same remarks apply to the theory of an absolute 
differentia, such as rationale, predicable of all men and 
of none but men, and serving to distinguish that species, 
not from some other given species, but from all others 
whatever. Porphyry, as has been before observed, ad- 



^ Between Nominalism and Conceptualism there is no real difference, 
unless in conjunction with the latter we maintain the power of the mind 
to form Universal notions, unaided by verbal or other symbols. And even 
then, all Nominalism will be Conceptualism, though all Conceptualism 
will not be Nominalism. For Universals can only be identified with names 
by considering these as the signs of notions. Yet Nominalism has been 
accused as destructive of all Philosophy, and that by the advocates of 
Conceptualism. But the fundamental error of Hobbes and his followers 
is not their doctrine of Universal Terms, but their theory of the import of 
Propositions. The two, however, are not necessarily connected. We may 
adopt Locke's theory of abstract ideas, without maintaining with him that 
knowledge is the perception of the agreement or disagreement of two 
ideas ; and we may hold that general notions require the aid of language, 
without maintaining with Hobbes, that truth and falsehood depend on 
names, or with Condillac, that science is only a language well constructed. 
But, not to argue this point here, we may observe, that the Scholasitic 
Nominalists, at least Abelard and Occam, were Conceptualists. With 
regard to Roscelin, it is hardly fair, upon the sUght notices we possess of 
his views, to identify his Nominalism with that of Hobbes, whom Leibnitz 
rightly calls plusquam Nominalis. No one can suppose Abelai'd's dedvctio 
ad absurdum to be a fair statement of Roscelin's views. 

M 



162 APPENDIX. 

mits only a relative differentia. His definition of man 
is Jojov Koytycov ^vr^rov ; rational being the differentia of man 
when compared with brutes; mortal, when compared with 
the Gods^. But if either of these attributes be selected 
as the differentia of man absolutely, we must again have 
recourse to Realism to justify the position. If species are 
made by Nature, they may have been so framed that each 
has a peculiar characteristic shared by no other. How 
this can be proved to be the case is another question ; 
but there is no a priori impossibility in the supposition. 
But if the species is but a conception formed by the 
mind, what is to hinder us from forming four complex 
notions, ahc, ahd, acd, bed, of which no part is a dif- 
ferentia absolutely and per se, though c distinguishes the 
first from the second, b the first from the third, and a the 
first from the fourth ? 

With regard to the doctrine of the Tnfima Species 
being the whole essence of the individuals of which it 
is predicated, the case is still clearer ; inasmuch as this 
language was expressly maintained by the Realists, and 
expressly repudiated by the Nominalists. It is true that 
it is previously to be found in Boethius ; but here his 
authority is of little value, as nothing can be more vacil- 
lating than his opinions on the whole question. Boethius 
wrote his Commentaries with the design of reconciling 
Aristotle with Plato : he succeeded only in contradicting 
himself. In one of his expositions of Porphyry he goes 
beyond Plato in Realism; in the other, he is a professed 
Conceptualist^ But even had his views been more 
definite in favour of the latter hypothesis, it would only 
shew that he admitted details into his system incon- 
sistent, if pushed to their ultimate consequences, with its 
main positions. 

B Isagoge, iii. 19. 

^ Cousin ^Ouvrages d'Abelard, Introduction, p. 66. 



APPENDIX. 163 

In treating the doctrine of Predicables, two alter- 
natives are open to the modern Logician. Either he 
may take the scholastic language as he finds it, and? 
explain it with reference to the theories on which it 
was originally founded ; warning, however, at the same 
time his readers or hearers, that the supposed Real 
Essences are deserving of the same amount of belief 
as the Deities of Heathen Mythology, or the Sylphs, 
Gnomes, and Salamanders of the Rosicrucians ; or he 
may adopt a theory of Universals in conformity w^ith 
views current in modern philosophy, and remodel the 
whole account of the predicables, so as to make it 
consistent therewith. But any attempt at a compromise 
between the two, any explanation of ancient language 
upon modern hypotheses, can produce nothing but in- 
consistency in the Teacher and confusion in the Pupil. 
In the first place, such explanation, even where most 
satisfactory, is founded merely on analogy, and hence 
will rather shew what the doctrines expounded ought 
to have been, according to modern criticism, than what 
they actually were. In the second place, the analogy 
in some important particulars will fail entirely, and 
the exceptional cases must either by some unnatural 
distortion be forced under the given classification, or 
be excluded altogether, to the serious detriment of the 
completeness of the theory. 

To adopt then the first mode of explanation. We will 
suppose that Genera and Species are substances, having 
a real existence independently of us, and cognisable as 
to their nature, no matter how, by the human mind. Of 
these universal substances, some are more extensive, 
others less so, the limits at both extremities being fixed 
by nature, and the numbers in each degree settled and 
unalterable. The higher enter into the composition of 
the lower, the lowest not contributing to form any other 

M 2 



../> 



164 APPENDIX. 

Universal, but susceptible of Accidents, from which union 
are formed various Individuals. Man, for example, is 
a lowest species ; to this are added certain accidental 
modifications which form Socrates, and at the same 
time others which form Plato. These modifications 
excepted, there is nothing in Socrates which is not 
at the same time in Plato, nor in Plato, which is not 
at the same time in Socrates'. Moreover, from these 
Universal Substances, or rather from the distinctive por- 
tion of each, certain qualities flow^ or are produced as 
eflfect from cause. Others, not connected bj causation, 
are found in the individuals of this or that Species, some 
universally in all, others partially, in some individuals 
only. 

From a series of assumptions of this kind, the expo- 
sition of the Realist doctrine of Predicables is easy. And 
this, or some other of the various phases of Scholastic 
Realism, must of necessity be assumed, if our intention 
is to explain an old theory, not to construct a new one. 
On the other hand, we have the modern Logician 

;. expounding somewhat in the following style. Genera; 

and Species have no existence a 'parte Rei, but are 

t ^ <T?' TQotions formed by the mind from observing certain 
points of similarity in different individuals. But simi- 
larity must not be confounded with identity. The image 
and superscription on two coins may present no dis- 
cernible marks of distinction from each other ; but if on 



' " Homo quffidam Species est, res una essentialiter, cui adveniunt 
formse quaedam et eflSicimit Socratem : illam eamdem essentialiter eodem 
modo informant formae facientes Platonem et csetera individua hominis; 
nee aliquid est in Socrate, praeter illas formas informantes illam materiam 
ad faciendum Socratem, quin illud idem eodem tempore in Platone infor- 
matum sit formis Platonis. Et hoc intelligunt de singulis speciebus ad 
indi%idua et de generibus ad species." Abelard, de Gen. et Spec. ed. Cousin, 
p. 513. Tliis was the first doctrine of William of Champeaux. Other 
expositions of Realism might be given. 



APPENDIX. 165 

that account we say that they are the same, "we employ 
the word in an equivocal sense, which must be carefully 
distinguished from that in which we say that both are 
struck from the same die. In the latter sense, the 
attributes forming the humanity of Socrates are not the 
same with those forming the humanity of Plato ; though 
the common notion man embraces both, and though, by 
availing ourselves of an ambiguity of language, we say 
that both are of the same species. 

General notions thus framed by the mind, when 
expressed in language, form common terms. And the 
various attributes comprehended'' in every such notion 
are its logical essence ^ By this we do not mean any ' 
thing necessary to the physical existence of an object; 
but merely that, as general notions are formed from 
the observation of similar attributes in individuals, every 
individual must possess such attributes, if it is to be 
included under the extension of the notion and called 
by the corresponding common name. Proper names, on 
the contrary, have no essence, as they have no general 
notion belonging to them, but are mere arbitrary marks 

^ In a Pamphlet published under the name of " A Dissertation on the 
Heads of Predicables," I inadvertently adopted BIr. Mill's expressions of 
connotation and denotation, to distinguish between the attributes contained 
in a complex notion, and the subjects of which it is predicated. The 
distinction I still regard as most important, and one that is not perhaps 
sufficiently marked in modern language ; but further study of the scholastic 
phraseology has led me to regaxd Mr. Mill's language as too wide a 
departure from the original use of the terms. For this reason I have 
preferred the expressions Comprehension and Extension, as better sanc- 
tioned by Logical authority. Cf. Port Eoyal Logic, P. I. chap. 6. " J'appelle 
comprehension de I'idee, les attributs qu'elle enferme en soi. J'appelle 
etendue de I'id^e, les sujets a qui cette idee convient." For the Scholastic 
Connotation, see p. 16, note g. 

' This is the Nominal Essence of Locke, which corresponds to the 
Logical Essence of other philosophers, though variously explained according 
to their different Metaphysical theories. The term Real Essence is used 
by the same philosopher to denote that generally unknown constitution of 
individual things on which their sensible properties depend. 



166 APPENDIX. 

imposed for the purpose of distinguishing individuals 
from each other. 

But though our earliest complex notions may have 
been gained from real objects, there is no reason why 
such notions alone should be admitted in a theory of 
Predication. Such a theory only distinguishes the several 
relations which the subject and predicate of a proposition 
may bear to each other. With the objective existence of 
things corresponding to our general notions, we have for 
the present no concern. Whatever theory may be adopted 
as to the origin of our ideas, there can be no doubt that 
w^e have the power of forming combinations in the mind, 
which have not been observed to exist in nature'". And 
the relation of subject and predicate in propositions into 
which such notions onter, may be identified with some of 
the relations of other notions. 

In constructing or explaining a theory of Predication 
in conformity with these views, there is one ambiguity 
which it is not possible to avoid, without a coinage of 
new terms. The distinctions of Genus and Differentia 
must be gained by comparing two terms not predicable 
of each other. Compare, for example, Man with Brute, 
the common Genus will be Animal, the respective Diffe- 
rentiae, Rational and Irrational. But there is no absolute 
Genus or Differentia, and frequently, while the whole 
comprehension of the notion remains the same, the Genus 
and Differentia may change places, according as it is 
compared with this or that other notion. In the com- 
parison, for example-, of a plane triangle with a paral- 
lelogram, " rectilineal figure" is its common, " having 
three sides" its distinctive part. But compare a plane 
with a spherical triangle, " having three sides" is common 
to both ; the distinction being, that the sides in the one 

"* Cf. Locke, Essay, b. ii. ch. 2. §. 2. 



APPENDIX. 167 

case are straight lines, in the other, arcs of great circles". 
But when one only of the compared notions is employed 
as the subject of a proposition, and a portion of the 
attributes which it comprehends is predicated of it, that 
predicate cannot properly be called Genus or Differentia, 
the comparison from which these distinctions arise having 
ceased. 

With this proviso, w^e may adopt, mutatis mutandis, 
the classification of the Predicables given by Aristotle 
himself, as furnishing a more satisfactory groundwork 
than either the Isagoge of Porphyry or its subsequent 
scholastic embellishments. Every Proposition, accord- 
ing to Aristotle, expresses one of four relations of the 
Predicate to its Subject; Genus, (under which may be 
included Differentia,) Definition, Property, or Accident**. 
For every Predicate must either be convertible with its 
Subject or not. If convertible, it either expresses the 
whole Essence {to t/ ^v shon) of the Subject or not. In 
the foi'mer case it is called Definition, in the latter, 
Property. If not convertible, it either expresses part of 
the Essence or not. In the former case it is Genus, in 
the latter. Accident. 

This division, being founded on dichotomy by contra- 
f diction, must necessarily exhaust every possible mode of 
Predication. Interpreting the Essence, in accordance 
with our present view, as the sum of the attributes 
comprehended in a notion, we shall find all four mem- 
bers admissible where the Subject of the proposition 

" This has been remarked by Leibnitz, Nouveaux Essais, iii. 3. p. 304, 
ed. Erdmann. Schreibeti an Wagner, p. 425. 

j o See Topics, i. 8. Sundry attempts have been made, not very success- 

fully, to reconcile this account with that of Porphyry. But though some 

I license of interpretation may be allowed, when the object is to reconcile 

I an author with himself, it is scarcely necessary to strain his language into 
agreement with a writer who Uved more than six centuries after him, and 

I who does not even profess to be commenting on him. 



16'8 APPENDIX. 

has both comprehension and extension; i. e. is a complex 
notion containing attributes, and is predicable of existing 
objects. For its Predicate may either express a whole or 
a part of the attributes comprehended in the Subject, or 
else some attribute not so comprehended, but possessed 
by the objects of which the Subject is pi-edicable. In 
the latter case, where the Subject and Predicate are 
distinct in comprehension, they may be either equal or 
unequal in extension. 

The two first cases will correspond to the class of 
Propositions called by Kant, Analytical Judgments, 
and by Mr. Mill, Verbal Propositions. In these th^ 
attributes composing the Predicate are a part or the 
whole of those composing the Subject. They therefore 
depend solely on the principle of Identity. If Animal 
form part of the conception Man, the objects, whether 
actual or possible, thought under the latter must neces- 
sarily be identical with a portion of those thought under 
the former. 

To avoid the introduction of new words, we may retain 
the Aristotelian nomenclature of Genus and Definition to 
express the relation of Predicate to Subject in these two 
classes of Propositions ; though the former appellation, 
for the reason stated above, is not altogether free from 
objections. Under Definition may be also included a 
class of Propositions which are not, in the strict sense of 
the word, Analytical^, and are not admitted by Aristotle 
to be Definitions proper; viz. those in which the Predicate 
is a single term synonymous with the Subject. 

The last two cases will correspond to the Synthetical 
Judgments of Kant, and to the Ileal Propositions of 
Mr. Mill. In these, the subject is neither a word nor 
a notion, but the several individual things of which 

p Though Kant admits even tautological propositions (A is^) as 
explicitly anah'tical. 



APPENDIX. 169 

a certain notion is predicable. For example, in the 
Proposition, " All men are mortal," we do not mean 
that the conception Man includes Mortality, but that the 
individuals possessing the attributes comprehended in 
the former notion possess also those comprehended in 
the latter. 

In distinguishing a certain portion of these Propo- 
sitions as predicating Property, we must divest ourselves 
altogether of the notion of necessary or contingent con- 
nexion, and regard the word purely as a translation of 
the Aristotelian 'ihov. These Propositions assert, not 
merely that certain objects possess certain attributes, but 
that they alone possess them. This assertion, however, t 
is very imperfectly expressed in the ordinary form of the 
affirmative proposition. The judgment, " all equilateral 
triangles are equiangular," does not by its mere form 
imply that all equiangular triangles are equilateral. This 
knowledge is conveyed by the geometrical matter, not by 
the logical form. To remedy this defect of language, it 
is necessary in a system of formal Logic to distinguish 
the propositions in which property is predicated from 
those in which accident is predicated, by attaching an 
universal sign to the predicate. " All equilateral triangles 
are all equiangular," will then denote that the predicate 
is a property of the subject ; while " all men are some 
mortals," distinguishes by the particular sign that the 
predicate is an accident. 

The distinction adopted by Aldrich between Property 
and Accident, as necessarily or contingently connected 
with the subject, is untenable in formal Logic. If not 
expressed in the copula, it implies the extralogical 
knowledge of a law of connexion existing or not between 
the objects signified by the terms; a law which cannot 
be indicated in the symbolical form of the proposition. 



1 70 APPENDIX. 

If, on the other hand, a special form of the copula is 
adopted, and Property and Accident distinguished by the 
expressions, A must he B, A may he B, the classification 
becomes no longer applicable to the pure form of the 
proposition, and requires the introduction of the extra- 
logical doctrine of Modality*^. The adoption of a 
quantified predicate, on the other hand, is a necessary 
step when language is designed to express the pure form 
of thought, and every classification of logical forms should 
be adapted to this condition ^ 

In the foregoing remarks, Genus and Definition ex- 
press a relation of notions to notions, Property and 
Accident, one of attributes to things. Hence it will follow 
that notions thought as unreal, i. e. confessedly predicable 
of no objects existing elsewhere than in the mind, can 
only, as such, be the subjects of analytical judgments. 
Proper names, on the other hand, having no essence, can 
only be the subjects of synthetical judgments. The 
former have no Properties or Accidents; the latter have 
no Genus or Definition. 

Species is excluded from the Predicables, and confined 
to the Species Suhjicihilis, the correlative of the Predicable 
Genus. By this we avoid an inconsistency of which the 
majority of Logicians are guilty, in employing the term 
Species sometimes to express a relation of a Predicate 
to a Subject, sometimes that of a Subject to a Pre- 
dicate. The so-called Species Prcedicahilis, is, in the 
manner of its predication, in no way distinguishable 
from Genus. Man, when predicated of philosopher, 
expresses a part only of the essence of its subject, i. ej 
a portion of the attributes which the subject notion 

n On Modality as a Form, see Prolegomena Logica, note G. 
^ This principle, the basis of Sk W. Hamilton's New Analytic, is well 
stated by Mr. Baynes, Essay on the New Analytic, p. 9. -~ 



APPENDIX. 171 

comprehends; precisely as does animal, when predicated 
of man, 

A Lowest Species will be inadmissible, as it implies 
a notion so complex as to be incapable of further 
accessions. It is true that, in the continual formation of 
Species, we may arrive at combinations of attributes not 
realized in Nature ; but the classification of things is not 
the province of the Logician ; nor has he a right to con- 
clude a priori that the field of physical research is ex- 
hausted, or that notions now regarded as imaginary may 
not hereafter be discovered to be real. But whether such 
discovery be made or not, it will not affect the relation 
of two notions to each other. Logic is concerned only 
with the necessary relations of concepts in thought. 
Every concept being common to a plurality of objects, 
is potentially divisible into lower ones. A logical 
lowest species, if such were possible, would be a con- 
cept embracing all conceivable attributes not condemned 
by the laws of thought as contradictory of each other. 
This, as well as its opposite the logical highest genus, 
or notion so simple as to have no distinctive attributes, 
are mere imaginary limits, never reached in any process 
of actual thought*. A material science may have its 
highest and lowest classes ; the former being the general 
class, embracing all the objects whose properties that 
science investigates ; the latter the classes at which that 
special investigation ends. In Geometry, for example, 
under the summum genus of magnitudes in space, we find 
three infimce species of triangles, the equilateral, the 
isosceles, and the scalene. The geometrical properties 
of the figures are not affected by any further subdivision. 
But this limitation cannot be acknowledged by the 
Logician. He knows nothing of the geometrical or 

* See Prolegomena Logica, p. 183. 



172 APPENDIX. 

physical properties of this or that class of objects. As 
a mere concept, " an equilateral triangle whose sides are 
two feet long," is a subordinate species to equilateral 
triangle ; and the subdivision may, as far as mere thought 
is concerned, be continued ad infinitum. 






APPENDIX. 173 



Note B. 
on the categories. 

Lists of the Categories, more or less complete, occur 
in different parts of Aristotle's works in slightly different 
relations. The following passages may be selected as 
the principal. Categ. ch. 4. Twv xara fiyjhfjuioiv <rvfji7rXoxY}V 
\syofx,evcov skokttov ^toi ov(riuv <n^(jt,ulvsi ij ttocov yj -ttoiov ri Trgo^ n 
>j Ttorj >j ttotI % xsioSai >j ep^£*v yj ttoisIv yj 7roi(r^?iV. "Ectt/ Se oucioc 
/x-ev wj TVTTM sWslv olov oivQgooTTOs, T-TTTrof TTotrov 8s olov 8i7r>jp^u, 
t^Ittyj^v TTOiOv 8e oiov Xsuxov. ygufjif/.otTixov' Trgog t» 5e olov 
hTTkoKTiov, rjfLKTv, jxsi^ov vov Ss olov Iv Auxs/o;, Iv ayogSc' ttots 
8e olov 6;)(;fl£j, 'TTsgvTiV xsi(r$on Se olov ocvotxsiToti, xa5»)Tar e%£*v Se 
olov u7ro8e§cTai, cw7rAio"Tar woislv 8e olov t6jU,v£<, xai'gi* Tracrp^giv §g 
olov TSfjivsTui, xotisToii. Tojfic. i. 9. Msra to/vuv tuvto. hi 
hogl(ru<rQai to. yevYj tmv xotTT^yogiaoVf Iv olg v7rag^ov<riv ul f>i^Qsi(ron 
TSTTagss. "EcTi he tolvtol tov ugi^^ov 8exa, t/ Io-t», Trocrov, ttoiov, 
7Fg6$ T«, TToD, -^rore, xsi<rQixi, e%£«v, ttoisIv, 'KOLdyzw. 'Asl ya^ to 
(TUfX^s^i^xos xal TO ysvog xoti to T^iov xal 6 ogKTfxog sv y^ia tovtoov 
Ta)V xocTY/yogiMV ecTcn' mS.a'ui yoig a\ Zia. tovtoov 7rgoTa(rsig y} t* 

IcTTIV Y) 'ffOlOV T^ TTOO'OV Yj TMV akKctiV T<V« XUTYiyOgiuiiV (TYll/^OtlVOVO'lV . 

Metaph. iv. 7. Kad' auTa 8e elvai ksysTon oa'airsg <TYjfjt,ulvei Toi 
(T^YifjiotTu TYjg xtxTYiyogiocg' hact.'/jhg yoig XeysToii, TOdoLOTayoig to 
e*vai (yi^fixivsi. 'FiTts) ovv toov xenTYiyogovfjt^evMv tu [j^ev ti Io-t* 

0">3jU,a/v£l, TCt 8s TTOiOV, TCt 8s TTOCTo'v, Tfit 8s TTgOf Ti, Ta 8s TTOielv )J 

Tzmyziv^ TU 8e TTOu, ra 8s ttots, IxacTw toutcov to elvai Tat5T0 
(Dj/xa/vsi. 

From these passages it appears that the Categories 
were regarded by Aristotle, 1. As an enumeration of i '/ 
the different significations of simple terms, apart from ^ 
their connexion in the proposition. 2. As an enurae-i 



174 APPENDIX. 

ration of the several genera under which Aristotle's four 
heads of predicables fall. 3. As an enumeration of the 
different modes in which Being may be signified. An 
examination of the principle of classification is neces- 
sary, in order that we may determine how far the charges 
of deficiency and redundancy, so frequently brought 
against Aristotle's list, can be fairly maintained. 

The most celebrated of these accusations is that of 
Kant^ Assuming that Aristotle's design was identical 
with his own, viz. to enumerate the pure or a priori 
conceptions of the understanding, he asserts that the 
classification was made upon no principle ; that it was 
found by the author to be defective, and the post- 
predicaments added in consequence ; that the list thus 
enlarged is still defective ; that it contains forms of the 
sensibility as well as of the understanding ; {quando, uhi, 
situs, prius, simul ;) that empirical notions are intruded 
among the pure (motus), and deduced concepts classed as 
original {actio, passio) ; and that some original elements 
are altogether omitted*'. 

A somewhat similar criticism is given in Mr. Mill's 
Logic. The Categories he supposes to be " an enume- 
ration of all things, capable of being named ; an enume- 
ration by the summa genera, i. e. the most extensive 
classes into which things could be distributed; which 
therefore were so many highest Predicates, one or other 
of which was supposed capable of being affirmed with 
truth of every nameable thing whatsoever." Thus viewed, 
he pronounces the list to be both redundant and de- 
fective. Action, passion, and local situation, ought to 
be included under relation ; together with position in 
time {quando), and in space {uhi) ; while the distinction 

^ For an account of the earlier criticisms of the Categories by Plotinus, 
Campanella, and others, see Trendelenburg, Geschichte der Kategorienlehre. 
^ Kritik der r. V. p. 80. (ed. Rosenkranz.) Prolegomena, §. 39. 



APPENDIX. 175 

between the latter and situs is merely verbal. On the 
other hand, all states of mind are omitted entirely ; as 
they cannot be reckoned either among substances or 
attributes ^ 

These objections will stand or fall, according as their 
authors have rightly or wrongly divined the purpose of 
Aristotle's classification. Kant is mistaken in supposing 
that Aristotle added the post-predicaments to complete 
his list of Categories. The post-predicaments were not 
so called by Aristotle, and have never been classed by 
commentators among the Categories. The term is of 
scholastic origin, and was employed to denote the five 
subjects treated of by Aristotle after the Categories 
proper. Kant is equally mistaken in supposing that 
Aristotle had any intention of classifying the pure forms 
of the understanding, independent of experience. On 
the contrary, the Categories belong to the matter of 
thought, are generalized from experience, and leave 
altogether untouched the psychological question of the 
existence of elements a priori^. Any objection, there- 
fore, based on the inclusion of empirical or the ex- 
clusion of original elements, is untenable, and rests on 
a misapprehension of the philosopher's design. Nor yet 
can we adopt Mr. Mill's opinion, that Aristotle designed 
a classification of all things capable of being named ; at 
least not in that point of view in which things are 
regarded according to their real characteristics as pre- 
sented to consciousness. The Categories are rather an 
i enumeration of the different modes of naming things, 
i classified primarily according to the grammatical dis- 
I tinctions of speech, and gained, not from the observation 

j '^ Mill's Logic, vol. i. p. 60. 

I '^ See Sir W. Hamilton, Edinburgh Review, No. 99. p. 211. Franck, 

Histoire de la Logique, p. 26. St. Hilaire, Logiqve d'Aristote traduite en 

Franqais, Preface, p. Ixxx. 



176 APPENDIX. 

of objects, but from the analysis of assertions. This is 
manifest from the name and from the manner of treat- 
ment. K.ocTYiyogiu, xtxTYiyogsiv, xaTYjyogYifxot, }caTri'yo^o6[x.svov, 
xoLTY^yoqiyio^, have all primarily reference to forms of 
speech ; the term naTYiyopia, being used by Aristotle as 
well for any predicate term, as for the highest gene- 
ralizations under which predicates can be classed ^ In 
the beginning of the treatise on the Categories, terms as 
combined in a proposition are made to precede terms 
regarded separately^; and the proposition, as the only 
assertion capable of truth and falsehood, appears to be 
regarded as the unit of speech, of which the simple term 
is but a fractional element^. 

It is therefore probable, that the Aristotelian distinction 
of Categories arose from the resolution of the proposition 
and a classification of the grammatical distinctions indi- 
cated by its parts. The noun substantive leads us to the 
category of oua-la, the adjectives of number and of quality 
to iroa-ov and ttoiov, the adjective of comparison to ^rgos ri, 
the adverbs of place and time to %oi^ and %ors, the different 
forms of the verb, intransitive, praeterite, active, and pas- 
sive, to Ksia-^cn, ep^sjv, TroisTv, and itoLdyzw^. It is true that in 
his subsequent treatment the philosopher by no means 
adheres strictly to the grammatical point of view, and 
that his classification may, even on his own principles, 
be considerably simplified ; but it must be remembered, 
that at that time the science of Grammar was in its 
infancy, that its forms of speech had not been analysed 
completely, nor its boundaries clearly separated from 
those of Logic and Metaphysics. 

f See Trendelenburg, Geschichte der Kategorienlehre, p. 2. The Aristo- 
telian expression (rx'^iM-ara rrjs Kar-riyoplas will thus primarily mean forms 
of predication. 

e See Catei/. ch. 2. 

h See Categ. ch. 3. Trendelenburg, Kategonenlehre, p. 12. -- 

' Trendelenburg, Elementa, §. 3. Kategorienlehre, p. 23. 



APPENDIX. 177 

The omission, therefore, in the Aristotelian list, of 
separate heads of classification for mental states, cannot 
be charged as a defect in this point of view, so long as 
mind and its various states (whatever may be their dif- 
ference in other respects) are represented by the same 
verbal forms as substances and attributes. And accord- 
ingly we find various mental states, faculties, passions, 
habits, and dispositions, classified together with corre- 
sponding affections of body, under the head of qualities''. 
A more valid objection in a grammatical point of view 
would be, that qualities in their abstract form are ex- 
pressed by nouns substantive, and should therefore be 
classed under the category of substance. This objection 
would be tenable in relation to the distinctions of modern 
Grammar. But Aristotle appears to have limited the 
substantive word to terms expressive of the irqchrai oixrlon, 
or individual substances, and the IsvTsqon oua-lai, or their 
several genera and species. The latter denote properly 
the category of substance, or substance considered as 
one of the possible predicates of a proposition. Words 
denoting individual substances, being subjects only in 
the proposition, do not properly indicate a category ^ 

In reference, therefore, to the treatise of the same 
name, we might fairly describe the Aristotelian Categories 
as an enumeration of the different grammatical forms of 
the possible predicates of a proposition, viewed in relation 
to the first substance as a subject. And this view is not 
materially departed fi'om in the other writings of Aristotle. 
The passage quoted from the Topics, indeed, only con- 
tinues the same view, stating that those predicates, which 
in their actual relation to their subjects in a proposition 



^ See Categ. ch. 8. 

^ Categ. 5. 27. 'Att^ fihvyhp rrjs irpdrris oixrias oi/Se/xia iarl Karrjyopla' kui' 
ovBevhs yhp xnroKeiixivov \ey€Tai' rwv Se SevTepccu ovcriuv rh fiev elSos Kara rod 
arj/iow KOTTiyopuTai, rh 5e y4vos Kal Korb. tov etSovs Koi Kara rod arSfiov, 

N 



178 APPENDIX. 

come under one of the four heads of Genus, Definition, 
Property, or Accident, come as simple terms under one 
of the ten Categories. The Metaphysical view of the 
Categories is not materially different. In that work, 
Aristotle enumerates the different senses in which the 
term Being (to ov) is used, in order to determine in what 
sense it is applied to the object of metaphysical in- 
quiries"*. Being sometimes signifies the accidental 
connection of an attribute with a subject, or of two 
attributes with a common subject. It is also used co- 
extensively with the Categories in predication ; thus we 
may say, uv^gooTrog uyia/vst, or avdgMTrog vyiulvcjov so-tIv, avSgco- 
7ro$ TS[jt,vsi, or avQgcoTros tsiji.vu)v Idxiv, the verb elvat being 
admissible as a copula in any proposition, whatever may 
be the category of its predicate ^ But substance is the 
vpooTcos ov, the proper object of metaphysics*'. In this 
account, Aristotle does not appear to have distinguished 
between the verb substantive, as denoting real existence, 
and the copula as denoting the coexistence of notions in 
the mind ; but, as in other places, the Categories are 
enumerated, not as an exhaustive catalogue of existing 
things, but as a list of different modes of predicating by the 
copula. They thus originally belong to Grammar, rather 
than to Logic or Metaphysics, though the treatment of 
later philosophers, perhaps in some degree sanctioned 
by Aristotle himself, has brought them into closer con- 
nection with the latter sciences, and overlooked their 
proper relation to the former^. 

" See Trendelenburg, Kategorienlehre, p. 167. 

» Metaph. iv. 7. 

«> Metaph. vi. 1. 

P Trendelenburg, Kategorienlehre, p. 216'. 



APPENDIX. 179 



Note C. 
on definition. 

In the nates to Aldrich's account of Definition, I have 
endeavoured to explain his language in conformity with 
the views most commonly found in Logical Treatises* 
But as these views differ in many respects from those of 
Aristotle, on which they are supposed to be founded, and 
as a correct account of the doctrines of that Philosopher 
will materially assist in the solution of more than one 
of those vexatce qucestiones which are most perplexing 
to beginners in Logic, I shall attempt a somewhat fuller 
exposition here. c ;-Ltj^cutt., 

In the second Book of the Posterior Analytics, Aristotle 
mentions three different forms of Definition, in the 
following words : "Ecttjv a^a 6^<o-jtxOf elj \Lh \oyog rov ri sUTiv 'j^/it-c^^ /'^ i^'^- 
oii/ciTrohsiKTog, si; §£ (TvWoyia-ixog tov ri fVxi, 'nraodsi hia.'^sgoov Trig 
uTiohi^soog, Tgkog ds tyiC too t/ scTTiV otTrohl^scjog <ruix-n:spci(TiJi,ot^. 
This passage is a concise summary of the whole Aristo- 
telian theory of Definition. Adopting it as our text, we 
proceed to comment as follows. 

A necessary preliminary to the determining the Real 
Definition of any object, (t/ Io-tj,) is'to ascertain that such _ 
object exists {on ta-ri). Otherwise our Definition will ' 
be merely a nominal one''. But we have two classes of ^ '^ -^^^^^^^ ''" 
definable objects, of which the existence is determined 
in two different ways, producing a corresponding variety 
in the form of the Definition. 

« Anal. Post. ii. 10. 4. 

*• Anal. Post. ii. 8. 3. 'ASvvaroy elSevai ri iffTiv, ayvoovyras ei iariv. 
Ibid. ii. 7. 2. 'AvdyKT} yhp rhv elS6ra rh ri eariv duOpcoiros ^ &\\o briovv, 
€l5ei/ot /col '6ti iffTiv rh yhp fi^ hv ovSeU olSev '6 ti iariv, aKXa ri fxkv 
(TTIfAaivei 6 ^^yosji rh ovofjia, '6rav efira; rpay4\a<{)05, ri S* tirri rlpayiha^os 
aZvvarov ilSevai. "" " 
' N 2 



180 



APPENDIX. 



.W^T^^ 



'^ I. Attributes, under which term are included all things 
belonging to any other Category than that of Substance. 
These exist only in Substances as their subjects, and 
their existence is properly determined by Demonstration''. 
When ascertained in any other way, we are said to know 
it only accidentpJly^. In the Demonstrative Syllogism, 
the minor term is the Subject, the major the Attribute ; 
the_Cause,,hjlxittjie_ofjwhict^^ jaffected, 

being the, middle^ term . When by such a Syllogism we 
have proved that all A is B, we know that the attribute 
B exists in the subject A. 

II. Substancas, which exist not in a Subject, but per 
se^. Of such the existence cannot be proved, but must 
be assumed, before any of their Attributes can be demon- 
strated. This assumption, under the name of Hypothesis, 
forms one of the Aristotelian a^xa», or Principles of 
Science, which must precede all Demonstration^. 

c Hence the Scholastic maxim, Accidentis esse est inesse. Cf. Aquinas, 
Opusc. xlviii. de Syll. Demonst. ch. 11» I have preferred the term Attri- 
bute to Accident, inasmuch as the latter is frequently appropriated in a 
special sense to such Attributes as exist only contingently, and are therefore 
indemonstrable. 

^ Eth. Nic. xi. i.4. orav ydp iras irKxrein] koI yvdopL/xot avr^ S}(rtv al apxcd, 
iirlaraTai' el yap fM^ fiaWov tou (TvpLitepdayiaTos, koto, ffviM^e^riKhs e|€i r^r 
iirKTriifiriv. 

^ Categ. 5, 18. Koiyhv Se Kara irdcrris ovaias rh (jltj iv inroKei/xevq} eJvai. 

f The following table of the Principles of Science may be xiseful to the 
reader. 

'ApxaL 



KOivaL (e| cSj') 
1 


XSiai. (vepl 3) 


a^idfiara 


1 
©eVets 


forming the original premises /ro?» 
which Demonstration proceeds. 






opKr/xol 


viroOeaets 


Definitions, which of the 

Subjects are real, of the 

Attributes nominal. 


Assumptions of the existence of ! 
the Subjects, as a necessary con- 
dition to their definition. 




[N.B. The Attribi 

sumed to exist, but 

in their Su 


ites are sot as- 
proved to exist 
bjects.] 



APPENDIX. 181 

In some passages, speaking in a stricter sense, Aristotle 
declares Substances alone to be capable of Definition §; , 
but in the wider sense of the term which prevails through- 
out the Posterior Analytics, it is applicable both to^ ^,^.//. <.. 
Substances and to Attributes. In both cases the inquirjg^/^v:, - A~. 
into the Definition of a thing is identical with that into ^ ^^ ax-c^-^ 
its cause ; with this distinction, that in the case of 
Attributes, the Cause is to be sought, not in the Attribute, 
but in its Subject; where as in th e ^ase of Substanses I 
whi(2k.exist^jfr 5^,.-th.e Cause.is to be SQughtiii themselves 
only^. 

Attributes are defined by the same cause which served^'*' ^' "^ 7 
as a middle term to prove their existence. This is the '^ a.^^<-<- 
mode of Definition described as auKkoyidiCo^ lax) ti scrrij^j^^i^^^ c*-- 
TTTooasi hoi(psgcjov tyiS <x7rohl^ecti$. As an example, be gives 
the definition of an eclipse. The moon is proved to be 
eclipsed, because the sun's light is intercepted by the 
earth. The same cause furnishes us at once with a 
middle term for demonstration, and with a definition of 
the attribute*. Why is the moon eclipsed? Because 

See Anal. Post. i. 2. 7. i. 10. 1. i. 32. 6. and Sanderson's Logic, b. iii. ch. 11. 
From this it will be seen that Mr, Mill has unjustly aecused Ai-istotle of 
maintaining that the science of Geometry is deduced from Definitions. 
(Mill's Logic, vol. i. p. 197.) Hence may also be explained the contradiction 
which Stewart professes to find in Aristotle's doctrines. (Elements, Pt. ii. 
ch. 3. sect, i.) The principles//'ow which Aristotle demonstrates, are Axioms, 
of which he gives as a specimen, " If equals be taken from equals, the 
remainders are equal." The necessity of assuming the existence of the 
subject is maintained by Aristotle as clearly as by Mr. Mill. Cf. also 
I Metaph. V. 1.2.x. 7. 2. 

j e e. g. Metaph. vi. 5. 5. Cf. Metaph. vi. 4. 12. 

j ^ Anal. Post, ii. 2. 5. Sxrnep ovv Xeyofx^u, rh ri iariueiSevai ravrS icTTi Kal 

dih tI eVrtJ/. Tovto 5' ^ a,Tr\cos Koi /xt] toov inrapx^vTwv ti, ^ tIxiv virapx^v'^f'iv. 
I Anal. Post. i. 24. G. ^ yap KaS* avrh virdpx^i ti, tovto avrh avT^ oXtiov. 
j * The reduction of this Demonstration to syllogistic form has been 

I variously attempted. The following is given by Aquinas, Opusc. 38. 
j '* Omne corpus naturale, illuminatum a sole, privatum luce a terrse objectu 
j deficit; luna est hujusmodi, ergo luna deficit." A more general, and so far 
i preferable, major premise, is given by Crakanthorpe, Log. hb. iv. cap. 4. 



182 APPENDIX. 

the sun's light is intercepted by the earth. What is 
an eclipse ? An intercepting of the sun's light from the 
moon by the earth. Thunder in the same way is defined, 
oivoa-^sa-ig Trugbs h vs^si, the answer to the question Sia tI 
^govTOL'y being Sia to uTroa-fSsvwa-Qcn ro Trug ev rco ve<pei. 

This kind of definition, as has been observed, differs 
from a demonstration in the position (fieVij) of its 
terms^ ; for it has the same terms (skKsi'^is, ocvTl<pgci^is, 
G-eXrjVYi, — ^govTYi, kitodQea-ig Trugog^ vs^og^) but not in the same 
order, and with some variety of grammatical form (tttcoo-jj ^). 
--^y^Zje- ^ T'^^ Definition, then, of an Attribute is to be found in 
its Cause. But the Aristotelian Philosophy recognises 
four Causes, and sometimes more than one of these is 
concerned in the production of the same effect. Which 
of these is to be taken as the Defiiiition ? In Anal. Post, 
ii. 11. Aristotle shews that any one of the four may be 
used as a middle term in demonstration ; but it by no 
means follows that each may be a Definition of the major 
term. On this point, Aristotle's opinion is not decidedly 



*' Omne corpus illuminatum ab alio, inter quod et corpus illuminans opacum 
corpus sic interponitur, ut umbra opaci corporis operiat et comprehendat 
corpus illurainatum, eclipsatui' seu privatur suo lumine." 

J The Definition is by some given as " an obscuration of light in the 
moon, caused by the interposition of the earth." But in this case, the 
major term of the DemonstratiTO Syllogism is not " eclipsed," but " ob- 
scured." If these two tenns are synonymous, the Definition is merely 
nominal, and the latter part superfluous ; if not, we do not define the 
attribute demonstrated (obscuration), but another (eclipse), contained under 
it asi species under genus. I interpret Aristotle's words as referring to the 
complex form of the Definition, as given in question and answer, or in a 
proposition — tI eariv ^KXei\pis ; avrlcppa^is virh yrjs' r] e/cAeti^ts icrnv auricppa^is 
vrrh 777s. So the third form of Definition mentioned An. Pr. ii. 10, resembles 
the conclusion of a Demonstration, as containing, in the same form, only 
the major and minor terms, {^povr-f}, v4(j>os) tj ^povrii icrri }l/6(pos iv v4(p€i. 
Aristotle's text is not decisive, the one view being rather supported by 
ch. 8. the other by ch. 10. The question is by no means unimportant; the 
attempt to reduce these Definitions to a pseudo-Genus and Differentia has 
fostered a grave error, which will be noticed hereafter. 

^ Pacius aud Waitz consider irrucns and Oeais to be sjTionymous. 



APPENDIX. ] 83 

/> 

expressed ; but it seems probable that he regarded the ^-^^-^^ 
formal cause only as available for the purposes of De- ^"^^v^ — 
finition. For a material cause, properly speaking, has 
no place in attributes, but only in physical substances^; 
and that which in the former is most nearly analogous 
to matter, viz. the necessary condition out of which the 
effect arises, may in such cases be identified with the 
formal cause. This Aristotle allows in the chapter in 
question, when he states that the material cause there 
instanced as a middle term is in fact the same as the 
formal™. The efficie nt and final causes seem to be ' 

l'^ excluded, as not being contemporaneous with their 

I effects, so that from the existence of the one we cannot 
certainly infer that of the other ''. Whereas the formal 

] cause is expressly distinguished as to r/ \y zivoa''^ and 
the examples given of it in Anal. Post. ii. 12. I. corre- 
spond exactly to those previously given as Definitions. 
The other causes only accidentally serve the same pur- 

: pose, in those instances in which they coincide with the 
formal p. 



' Metaph. vii. 4. 6. Flepi ix\v ohv tols (pvcriKas ov(rias Koi yeuuT^ras h.v6.yKr\ 
O0TCO fierievai, et ris /ncTeicriv opdws, e^nep &pa atrid re toOto kuI roa-avra, Koi 
I Set Toi aXTia yuoopi^eiu. 'Eirl 5e tcDj/ (pvaiKwi/ fxkv al5iwu Se oixricov &\\os \6yos. 
''laus yap euia ovk exet v\7]u, fj oh Toiavrrjv aK\a [m6uou Kara rSirov Kivr]T-f]y. 
OvS' '6(ra 5^ (pvcrei fjLcv fiii, ovcla Se, [sc. virdpx^t] ovk ecrri tovtois 
v\r) aWa rh viroKelfiev ov rj ovaia. OTou ri aXriov eKKei^pews, tIs 
S\7i ; ov yap etTTiv, a\\' r} aeXi]vyi, '''^ irdcrxov. 

"" See Anal. Post. ii. 11. 3. 

n See Anal. Post. ii. 12. 3, 4. and Waitz, Org. vol. ii. p. 411. 

« Anal. Pr. ii. 11. 1. Metaph. i. 3. 1. 

!P See Rassow, "Aristotelis de Notionis Definitione Doctrina," p. 16. 
A very different view has been taken by some Logicians. Crakanthorpe, 
j for example, maintains that Demonstration can only be, " a causa eflSciente 
per emanationem, vel a causa efficiente per externum actionem, vel a causa 
finali;" and he devotes a chapter to shewing that neither the Material 
nor the Formal cause can be a middle term in Demonstration, though 
the efficient cause of the Attribute may be the formal cause of the 
Subject. A similar view is maintained by Sanderson, lib. iii. cap. 15. 



^/^ id 



^t^^i. * 



n 



184 APPENDIX. 

We have next to consider the Definitions of Sub- 
stances. Here too the investigation of cause is the 
root of the whole inquiry; but the manner in v^^hich it 
is conducted is not at first sight so obvious as in the 
former case. To ask the cause of an attribute, is to ask 
why the subject is so affected. Why, for example, is the 
moon eclipsed.? But what is meant by the^coMse of .a 
"^ an, and i n wh at form will the , giiPRtif^Ti bp proposed ? 
To ask why man exists, is in fact to ask why there are 
such beings in the world,— a question admitting only of 
Grangousier's solution "i, — and, when so solved, contri- 
buting nothing towards the Definition. To ask why a 
man is a man, is, as Aristotle himself observes, futile ^ 
The only form in which the question can be put is. Why 
is this or that individual a man ? What are the essential 
constituents of the notion Mail, the possession of which 
entitles Socrates to be reckoned in the class ? Here too 
the formal cause determines tbe Definition. 

These Definitions form the first of the three kinds 
'^> distinguished in Anal. Post. ii. 10. 4. ^^.fl-Tiv 0.00. ooio-fLo^ sic 

jjt^e v Xoyog To^j^tJ ^Tiv avcarohix Toc. These Definitions are 
assumed prior to all demonstration', and are real, inas- 
much as the existence of the objects is assumed with 
them. The ground of the assumption will vary according 
to the nature of the object to be defined*. 

With regard to the third class of Definitions, described 
as -T^j Tov r/ scTTiv oiTTohl^sMs (TvifMsqcKTi^a, Commcutators 



But to support this interpretation requires considerable straining of 
Aristotle's language. 

q Tristram Shandy, vol. iii. ch. 41. see also Rabelais, liv. 1. ch. 40. 

•■ Metaph. vi. 17. 2. rb [xhv oZu Sia ri aiirS iariy uvtS, ovdiv ia-ri (riTelv. 

* Anal. Post. ii. 9. 1. &<Tre 5t)\ov Sti koI rav t( icm ra fiev ^fieaa Koi apxo-i 
flffiv, t Koi eTj/ot /col rl icTiv viroQeadai Set ^ &\\ou rpSirov (paveph. iroi^crcu. 

' Metaph. x. 7. 2. Aajx^dvovai Se rh rl icTiv at fxkv \_iinaTrnxai] Sia rrjs 
alffd-fjcecos at S' inroTidefxeuai,' Sih /col StjKou e/c ttjs TOiavnjs iiraycoyijs oTi rrjs 
ova-las Kol tov tI iffriy ovk icrriv airSSei^is. 



APPENDIX. 185 

are at issue, whether they are to be regarded as nominal, 
or as imperfect real definitions^. The question is of the 
less importance, inasmuch as Aristotle elsewhere con- 
demns the use of such definitions altogether ^ The 
weight of authority is perhaps with the latter interpre- 
tation. But, judging merely from the text of Aristotle, 
the former seems far simpler and more natural y. 

From the above statement it would appear that Nominal ^ 
Definition, according to Aristotle, is one in which there 
is no evidence of the existence of objects to which the 
definition is applicable. In form it need not necessarily 
differ from a Real Definition. There may be a quasi- 
genus and a quasi-difference, as if we defined a centaur, 
" an animal with the upper parts of a man and the lower 
parts of a horse ;" but, until we have ascertained the 
existence of creatures possessing these characteristics, 
the definition is only one of the signification of a name^. 

tt Of the former opinion are Averroes and Zabarella, who are followed by 
M. St. Hilaire in his Translation of the Organon. The latter is maintained 
by the Greek Commentators, by Pacius, and in the recent Essays by 
Eassow and Kiihn. 

» See De Anima, ii. 2. 2. 

y The decision partly depends on the interpretation of a doubtful 
passage, Anal. Post. ii. 8. 4. rh 5' et effTiv ore /xe;/ Kara (rvixfiefiriKhs ^xofieyy 
dre S' exofxes ri avrov tov irpdyfiaros. The instances which follow may 
.refer either to the one or the other. 

* It may be questioned whether the name Nominal Definition is sanc- 
tioned by Aristotle. Trendelenburg indeed (Elementa, §. 55.) so renders 
the \6yos oi/o/xarciSTjs of An. Post. ii. 10. 1. and the interpretation, if correct, 
would seem to shew that Nominal, as well as Real Definitions must be 
sentences; but the context, x6yos rov ri (Tr]fxaiv€i rh ovo/jLa ^ \6yos 'inpos 
6vofjLard!>5r]s, seems rather to mean, " a sentence explanatory of the signifi- 
cation of a name, or of another sentence ha^dng the force of a name." On 
the other interpretation, the word eVepos is superfluous, and the example, 
oTov rh rt crrjfialvei ri icrrip ^ rpiycovov, unintelligible. By x6yos oi/oyuorc^Srjs 
is therefore meant a sentence whose signification, like that of a single noun, 
.is one. Such are all real Definitions, of which the example is a specimen. 
See De Int. 5. 2. Metaph. vi. 4. 16. vi. 12. 2. vii. 6. 2. Alex. Schol. p. 743. 
a. 81. In the Greek Commentators, on the other hand, \6yos ovofiardSris 
is clearly used for Nominal Definition. See Philop. Schol. p. 244. b. 31. 



186 APPENDIX. 

There is also no warrant in Aristotle for limiting the 
means by which Nominal Definition may be effected; 
as is done by those Logicians who specify synonyms and 
etymologies. The latter method indeed seems to have 
trespassed on the domain of Logic from that of Rhetoric. 
Nor has it the slightest connection with the former, save 
by an ambiguity of language. The etymology will in nine 
cases out of ten declare, not the present meaning of the 
word, but either one that has become obsolete, or some 
secondary notion, which may account for the imposition 
of the name, but which at no time formed, strictly speak- 
ing, any part of its signification. This holds equally of 
real objects and imaginary. It is only by an equivocation 
that " bull-piercer" can be assigned as the meaning of 
" centaur," or the notions of a swine and a quickset fence 
be combined into that of " hedgehog." 

Definition by synonym, on the other hand, may be one 
^f the means of explaining the signification of a name ; 
though relatively only, and from the accidental circum- 
stance of one word being more familiar to the hearer 
than another ; in which respect all translations from one 
language into another are equally nominal definitions. 
It is not, however, specially mentioned by Aristotle^. 
As a real definition it is obviously inadmissible, as it 
neither assigns the cause of a phenomenon nor developes 
the contents of a notion. 

The above data will also furnish us with an answer to 

^ci-^^/i-^^^ question, which, latterly at least, has been a sore puzzle 

to the tyro in Logic. What are the limits of Definition ? 

If all real Definition must be by Genus and Differentia, 



a Synonyms are expressly denied to be real Definitions in the proper 
sense by Aristotle, Top. I. 5. 1. though admitted to be bpiKd. As Nominal 
Definitions, they are allowed by Alexander on Metaph. vi. 4. p. 442. ed. 
Bonitz; but the genuineness of this portion of the Commentary has been 
questioned. 



:a ^ 



APPENDIX. 187 

the object defined must in every case be a Species. Summa, Y-c^y^/^''^^^^ 
Genera and Individuals are in that case alone inde-^^^/u^ ^ 
finable. And for this limitation, the authority of Aristotle 
may be cited. On the other hand, Locke ^ assures us 
that this restriction is erroneous, and that Simple Ideas 
alone are incapable of Definition ^ The dispute may be 
reduced to a mere verbal question. For Aristotle does 
not maintain that all Definitions must be by Gen_us_ajid 
Differe ntia, but only tho se of S ubstances. In the pas- 
sages which seem to extend this rule, Definition is used 
in the narrow sense which has been previously men- 
tioned*^. For it is obvious, to take the instances adduced 
above, that " quenching" cannot be called the genus of 
" thunder," or " interception" of " eclipse," in the same 



'» Essay, b. iii. 4. 7. But Locke has in this matter been anticipated by 
Descartes, Princip. i. 10. Sir W. Hamilton (Eeid's Works, p. 220.) main- 
tains that Aristotle has said the same thing. It is dangerous to dispute 
any thing which a man of Sir William's learning professes to have dis- 
covered in so wide a field as Aristotle, especially as he gives no references ; 
but if the passage alluded to be Metaph. vi. 17. 7. one might be tempted to 
hazard a different interpretation. T^ aTrAa seem rather to be the elements, 
(o7r\a adofiaray Met. vii. 1.2.) which have not, like compound substances, 
received a definite form, and thus are not definable. Cf. Plato, Theaet. 
p. 205. c. But the words are not sufiiciently decisive to furnish much 
ground for any theory. A more remarkable passage occurs in Occam's 
Logic, Pt. i. ch. 23. " Ex praedictis sequitur quod nulla intentio quae est 
prsecise communis rebus simplieibus carentibus compositione ex materia et 
forma habet diiferentias essentiales ; quia non habet partes, quamvis possit 
habere multas differentias accidentales. Ex iUo sequitm- ulterius quod 
nulla species quae est praecise simplicium est definibilis definitione proprie 
dicta, sive sit in genere substantiae sive in quocunque alio praedicamento." 
This," coupled with Occam's Conceptualist theory of Universals, is not very 
different from Locke's position concerning Simple Ideas. 

c By Simple Ideas, Locke meant all ideas derived immediately from 
sensation or reflection. In the formation of these the mind is wholly 
passive, whereas in the formation from them of Complex Ideas, it is active. 
Among Simple Ideas derived from sensation, he enumerates solidity, 
space, figure, rest, and motion ; from reflection, perception and volition ; 
from both, pleasure and pain. 

^ As, for example, Topics, i. 8. 3, Compare Metaph. vi. 4. 12, 16. vi. 5. 5. 
and Alex, in Metaph. p. 442. 30. ed. Bonitz. 



188 APPENDIX. 

sense as " animal" is of " man." Whereas Locke's simple 
, ,'Uu.:xf^ ideas are exclusively ideas of attributes. By reference 
i^'/.r w-'^'T^then to Aristotle's account of the latter, it will plainly 
v:^ ^'--^ appear that he and Locke mean two very different things 
- -i^at-'/ww^by Definition. With the former, it is an investigation 
IJ'Culo*^'^ ' '4. of the objective cause of a phenomenon ; with the latter, 
^j^_ , . ^ an analysis of the subjective impression which that 
/ ^phenomenon produces in the mind. The idea of an 

' ^j interception of light is not part of the idea eclipse, but 
the one phenomenon is the physical antecedent and 
cause of the other. Inquiries of this kind are still 
classed among the most important problems of Physical 
Science. What, for example, is light.? Is it a succession 
of material particles, or the undulations of an elastic 
medium ? The solution of this question would not be 
a Definition in Locke's sense of the word ; i. e. it would 
not be an analysis of the idea of light produced in the 
mind by sensation. The same may be said of colour. 
The mental sensation of whiteness or redness is altogether 
unaffected by the researches of Optics. The external 
cause of colour, regarded as a quality of bodies, falls 
directly within the province of the Science ^ The de- 
termination of such problems will be, in Aristotle's sense^ 
of the term, Definition. 

This may be further illustrated by reference to a dis- 
cussion of Aristotle's which few probably have perused 
for the first time, without considering it as singularly 
vague and unsatisfactory. I mean the dissertation on 
Pleasure, in the tenth Book of the Nicomachean Ethics. 
We are struck with the absence of any thing like a 
Definition or Analysis of the emotion ; and a reader who 
commences the study of the book with some previous 
knowledge of Locke's theory of Simple Ideas, will 
probably be disposed to regard it as an attempt to define 
e Compare on this subject, Reid, Inquiry, ch. vi. sect. 5. 



APPENDIX, 189 

that which is incapable of definition, and which in con- 
sequence necessarily involves its own failure. The same 
may be said of the principal opinion which Aristotle 
controverts. Whether we regard Pleasure with Plato, 
as consisting in a motion towards a natural state of 
harmony, or with Aristotle, in the perfect exercise of a 
power; neither of these can be termed an explanation 
of the feeling itself, but only of the cause by which it is 
produced. Pleasure itself remains an indefinite some- 
thing, consequent on the one or the other. Yet examined 
according to Aristotle's own view of the definition of ' 

attributes, we see that pleasure is as fairly defined by 
the perfection of the exercise of power, as an eclipse by 
the interception of light ^ 

There are, however, conditions and limits to thei/u^^ (^^-i^^. 
definitions of Attributes, though they are not the sameviic^x^^^i-il^ 
as those of Substances. Every Substance to be definable -ru^^, /T *V^^ 
must be a Species, Every Attribute must be Si Property , ^-^^.( '^y^ 
i. e. must be capable of demonstration by its cause. ^.^^^'^-^ a\i^ ^ 
Accidents then, as merely contingent attributes, are . ,,^ 
incapable of definition. This limitation, however, is 
merely relative to the degree of our knowledge of the 
matter. The advance of Science may transform Acci- 
dents into Properties, and thus furnish the requisite 
means of definition. 

Before concluding the subject, it will be necessary to 
say a few words on two other points connected with 
Aristotle's doctrine of Definition. 



*■ Leibnitz adopts the same view as Aristotle, observing that pleasure 
admits of a causal, though not of a nominal definition. Nouveaux Essais, 
ii. 2] . §. 46. In another point of view, simple ideas admit of a definition by 
logical analysis; viz. when they are considered, not as phenomena presented 
to the sense, to be resolved into simpler sensible phenomena, but as con- 
cepts, or general notions, representative of objects of thought, to be resolved 
into simpler concepts. On this distinction I have remarked elsewhere. 
See Prolegomena Logica, p. 45. 



190 APPENDIX. 

vT<f«--— -*- The first of these is his method of investigating, or, 

^"^ as he terms it, hunting for ^ the Definition. This may be 

effected in two ways, commonly called the methods of 
•C^u^i^ ^Division and Induction. The first of these consists in 

taking a wide Genus, under which the object to be defined 
is evidently included, and contracting it by the addition 
of successive differentiae, till we obtain a complex notion 
coextensive with that af which the Definition is sought. 
Of the notion thus obtained, each separate part is more 
extensive than that which is to be defined, though the 
whole is not so^. A good example of this method is 
given by Cicero, Topica, c. 6. " Sic igitur veteres praeci- 
piunt: cum sumseris ea, quae sint ei rei, quam definire 
velis, cum aliis communia, usque eo persequi, dum pro- 
prium efficiatur, quod nullam in aliam rem transferri 
possit. Ut hoc, Hereditas est pecunia. Commune 
adhuc : multa enim genera sunt pecuniae. Adde quod 
sequitur: quae morte alicujus ad quempiam pervenit. 
Nondum est definitio: multis enim modis sine hereditate 
teneri mortuorum pecuniae possunt. Unum adde verbura, 
jure : jam a communitate res disjuncta videbitur, ut sit 
explicata definitio sic : Hereditas est pecunia, quae 
morte alicujus ad quempiam pervenit jure. Nondum 
est satis ; adde, nee ea aut legata testamento, aut pos- 
sessione retenta : confectum est." 



s Anal. Post. ii. 13. 3. Tct 5^ TotoCra Xtjittcov fiexpi tovtov, €ws roffavra 
\'r](pd'p irpSnou, wv eKaarov fxey i-Trl ttX^^ov virdp^ei, airavra 5^ fi^ inl irKiov' 
ravrnv yap avdyKri ovcriav elvai rov irpdyfiaros. Yet in the Metaphysics 
(vi. 12.) he seems to maintain that the last differentia must he co- 
extensive Tvith the suhject; a view generally adopted hy the Scholastic 
Logicians, though manifestly inconsistent, not only with the passage ahove 
quoted, but with the example appended, rh Se reKevralov Koi rfj dvdSi. In 
the Metaphysics however he seems to he speaking, not of the specific 
difference per se, hut of the difference regarded as dividing the genus. 
But this is in fact equivalent only to saying that the whole must be co- 
extensive ; which no one would think of denying. 



APPENDIX. 191 

This method was a favourite with Plato ; it was rejected 
as useless by Speusippus^. Aristotle adopts an inter- 
mediate course, limiting, however, its utility chiefly to. ^^ 
two points, — the right arrangement of the several parts [. O]^^ 
of the Definition, and the security that nothing essential 
is omitted. It would thus seem to be useful, not so 
much for discovering Definition s^jas iox Resting Jiitx^va^ \ 
and even in this respect will be applicable only to one 
class of Definitions, that of Substances by genus and 
differentiae. iSu. 

For discovery, the second method is employed. This*^^ '^'^^^'^^^^^ 
is commonly called the Inductive Method; a name, how- 
ever, not sanctioned by Aristotle himself^. It consists in 
examining the several individuals of which the term to 
be defined is predicable, and observing what they have 
in common. If we can obtain one common notion, that 
is the Definition sought ; if not, the object of inquiry is 
not one but many. This method is equally applicable 
to Substances and to Attributes, though Aristotle only 
gives an example of the latter, the definition of mag- 
nanimity, gained by examining into the actions of dif- 
ferent magnanimous persons. 

Another important remark of Aristotle's is, that although, 
as we have already seen, demonstration, in certain cases, 
must always precede definition, yet no definition, as 
such, can be proved. This he maintains at some length 
(against Xeno crates''), in Anal. Post. i. 4. and shews that 



h See SchoHa, p. 179. b. 40. 248. a. 11. 

> This is perhaps mai-ked by Aristotle's own language. In reference to 
the one method, he uses KOTO(r/c€uc(^eti' ; to the other, ^77x6?^. 

J Aristotle does not give any name to the process ; by his Commentators 
it has been variously denominated the method of Resolution, of Com- 
position, of Induction. Cf. Edinburgh Review, No. 115. p. 236. ZabareUa, 
Logic, p. 1212. Pacius on Anal. Post. ii. 13. 21. 

^ Scholia, p. 242. b. 35. Trendelenburg.de An.p. 273. Kiihn, de Notionis 
Definitione, p. 11. 



192 APPENDIX. 

every attempt at such demonstration necessarily involves 
a petitio principii. The reason is obvious: since a 
definition can be predicated essentially (Iv tm tI so-ti) of 
nothing but that of which it is a definition ; and since, 
to prove a conclusion concerning the essence, the pre- 
mises must be of the same character ; the middle term 
assumed must be identical with the minor, and the major 
premise with the conclusion. 

Such is Aristotle's theory of Definition. Its funda- 
mental principle may still, mutatis mutandis, be retained, 
notwithstanding that the speculations of modern philo- 
sophy have considerably modified his distinctions of 
Substances and Attributes. Properly speaking, indeed, 
all Definition is an inquiry into Attributes. Our com- '; 
plex notions of Substances can only be resolved into I 
various Attributes, with the addition of an unknown • 
substratum: — a something to which we are compelled toi 
regard these Attributes as belonging^ Man, for example, 
is analysed into Animality, Rationality, and the some- 
thing which exhibits these phenomena. Pursue the 
analysis, and the result is the same. We have a some- 
thing corporeal, animated, sensible, rational. An un- 
known constant must always be added to complete the 
integration; unfortunately we have no means of de- 
termining its value. Still, this does not affect the basis 
of the Aristotelian distinction. For some phenomena 
can be accounted for by other phenomenal causes ; in 
others, we must acquiesce in the conviction that they are 
so, merely because they are. It is clearly impossible 
for the mere hypothesis of an unknown substratum to 
explain the reason of all the variety of attributes which 
different objects exhibit. 

One further question remains. How far Definition 
properly belongs to the province of Logic, was, as^we 
' Cf. Locke, Essay, book ii. ch. 23. 



APPENDIX. 193 

have seen, an early point of dispute among the School- 
men™. On this question the authority of Aristotle is of 
little avail for either side. That his treatment of the 
subject has far more of a material than a formal character 
is undeniable. And to those who maintain that the 
Organon of Aristotle is designed as a systematic treatise 
on a single subject called Logic, such testimony must be 
decisive as regai'ds both the material character of much 
of the Science, and its inclusion of Definition. But 
then it remains, and probably will continue to remain, 
a problem, to frame a conception of Logic adequate to 
the province thus assigned to it. This question has been 
already treated of in the Introduction, and need not be 
repeated here. It is sufficient to say that, as far as any 
evidence is furnished, either by the writings of Aristotle 
himself or by external testimony as to their original 
connexion, it is no more a departure from the authority 
of the Stagirite to assign a field to Logic incom- 
mensurate with that of the Organon, than it is to write 
a moral treatise on the basis of the Ethics, without 
including the Politics. Leaving then the question of 
authority, we may fairly assert that Logic as a formal 
Science can take no cognisance of the following 
points. 

I. It has nothing to do with determining the physical 
existence of attributes in their subjects ; which is in fact 
an inquiry into the material truth of the propositions in 
which such attributes are predicated. It is true that such 
propositions are by Aristotle considered as the conclusions 
of Syllogism, and so far their truth is merely formal. But 
it must be remembered, that no attribute can be syllogis- 
tically demonstrated of one subject, without being in the 
premise asserted of another ; and it is upon the material 
truth of the latter proposition that the certainty of the 
•" See p. 39, note o. 
O 



194 APPENDIX. 

former, and the demonstrative character of the whole 
reasoning, ultimately depends. 

II. Logic has nothing to do with testing the material 
correctness of a definition, i. e. ascertaining how far the ^ 
notions developed in our analysis of a given concept 
correspond to the principal phenomena exhibited by the 
objects usually included under that concept; nor even 
with the inquiry, whether our usage of terms corresponds, 
with the ordinary language of others. 

III. Still less does it lie within the province of Logic 
to perform the functions either of a Dictionary or of an 
Index to Physical Science ; to convey, that is, information 
from without, whether concerning the meaning of words 
or the nature of things, into a mind previously ignorant. 
Whereas, from the statements of some Logicians, one 
might almost imagine that they regarded their Science 
as furnishing, as it were. Logarithmic Tables of things in 
general ; Catalogues of Genera and Differentiae, to which 
w^e have only to refer any given object, to obtain full 
information concerning if". 

These being excluded, the only office that remains for 
Logic to perform, is to contribute to the distinctness of a 
given concept, by an analysis and separate exposition of 
the different parts contained within it. This operation is 



n Thus Melanchthoii; Erotemata Dialectica, p. 109. '« Cum quserimus 
definitionem inspiciuntur tabulae prsedicamentorum. Unde disces an res, 
de qua dictui^us es, sit substantia an accidens. Et si est accidens, in qua 
parte sit, in corpore an in anima, &c." And so Keckermann, Syst. Log. 
Mill. lib. i. cap. 17. " In hunc enim usum istse rerum tabulae et deli- 
neationes praecipue illic adumbrantur, ut definitum quaeratur, simulque 
animo lustretur, quid ex parte superiori proxime definite adjaceat; id 
enim erit ejus Genus : e. g. cupio conficere definitionem Hominis : cogito 
ergo primum in quo praedicamento sit Homo, et deprehendo ex notis Sub- 
stantias, esse in praedicamento Substantias: quocirca tabulam hujus prae- 
dicamenti perlustrans animo, deprehendo hominem proxime collocari sub 
animalir hinc concludo hoc esse pi'oximum ejus genus. Sic in aliis pro- 
ceditm- definitis per singiila preedicaraeuta." 



APPENDIX. 195 

analogous to that of drawing formal inferences, virtually 
contained in their premises, though not explicitly de- 
veloped". It is a process of self-examination, not dis- 
similar to the Platonic application of Dialectic, though 
widely differing as regards the objective truth of its 
results. For the Logical process furnishes only a sub- 
jective criterion : it enables us to represent more dis- 
tinctly to the mind, the notions previously existing there 
in more or less confusion : its rules direct us to compare 
concepts one with another, and furnish some security 
for our own consistency in employing them ; but they do 
not enable us to ascertain their accordance with externalj' 
objects, or to add the deficient parts, where they are 
inadequate representatives of the latter. The mind, like 
the sky, has its nebulse, which the telescope of Logic 
may resolve into their component stars. But here the 
parallel ceases. The Logical instrument discovers no 
luminary whose rays have not previously entered the 
eye ; it tells us nothing of their relative distances, of 
the velocity with which their light travels ; of any thing, 
in short, which did not form a confused portion of the 
sensuous representation p. This may seem but beggarly 
service to be performed by the Art of Arts and Science 
of Sciences. Inferior certainly it is to the gigantic pur- 
poses which more than one Logical Titan has essayed 
to accomplish with the same instrument. But let not its 
legitimate uses be contemned, because it has abated 
somewhat of the " vaulting ambition which o'erleaps 
I itself." It furnishes the mould by which the ever- 
' accumulating matter of consciousness is reduced to form 
i and consistency; it were ungrateful to despise it, because 
I it does not also dig the metal itself from the mine. 



« Cf. Anal. Post. i. 24. 11. p Cf. Kant, Logik, Einleitung. V. 

o 2 



19(> appendix. 

Note D. 
on material and formal consequence. 

A Material Consequence is defined by Aldrich to be 
one in which the conclusion follows from the premises 
solely by the force of the terms. This in fact means, 
f rom some un derstood Proposition or Pr opositions, cqn- 
necting the terms, by the addition of which the mind is 
enabled to reduce the Consequence to logic al form. This 
is easily seen, both in Aldrich's example, " Homo est 
animal. Ergo est vivens," and in the rather more com- 
plicated instance given by Sanderson, " Socrates est 
risibilis, ergo, Aliquis homo est rationalis." The latter, 
when the necessary conditions are supplied, is expanded 
into two syllogisms. 

Omne risibile est rationale ; 

Socrates est risibilis, 
Ergo, Socrates est rationalis. 

Socrates est homo. 
Ergo, Aliquis homo est rationalis. 

The failure therefore of a Material Consequence takes 
place when no such connexion exists between the terms 
as will warrant us in supplying the premises required : 
i. e. when one or more of the premises so supplied would 
be false. But to determine this point is obviously 
beyond the province of the Logician. For this reason, 
Material Consequence is rightly excluded from Logic. 

Moreover, even where true premises can be added, 
and the Consequence legitimately deduced, we cannot, 
except from knowledge of the matter, determine into 
what form the reasoning will naturally fall. In^ some 
cases, as in the example above quoted fi*om Sanderson, 



APPENDIX. 197 

the proof may be given in Categorical Syllogisms. In 
others, it is far more naturally exhibited in the hypo- 
thetical form. A hypothetical premise is sometimes 
the only materially allowable assumption in cases where 
the given antecedent and consequent have both terms 
distinct. E. g. A is B, therefore C is D. We may supply, 
If A is B, C is D ; but to determine the truth of the 
assumed proposition, whether it be hypothetical or 
categorical, does not fall within the province of the 
Logician. It may be questioned, however, whether the 
mere assumj^tion of a hypothetical premise can make a 
material consequence formal. See below, Note I. 

Among these material, and therefore extralogical, 
Consequences, are to be classed those which Reid 
adduces as cases for which Logic does not provide ; 
e. g. ^' Alexander was the son of Philip," therefore 
" Philip was the father of Alexander ;" '' A is greater 
than B," therefore " B is less than A." In both these it 
is our material knowledge of the relations " father and 
son," " greater and less," that enables us to make the 
inference. 

Another of Reid's examples is the following: '* A is 
equal to B, and B is equal to C, therefore A is equal 
to C." This reasoning is elliptical, and therefore, as it 
stands, material; though owing to the suppressed premise 
being self-evident, its deficiency is apt to be overlooked. 
Stated in logical form, the syllogism runs thus : 

Things that are equal to the same are equal to each other ; 

A and C are equal to the same, 

Therefore A and C are equal to each others 

Another example of the same kind is that sometimes 
called reasoning a fortiori. E. g. " A is greater than B, 

» Hamilton on Reid, p. 703. 



]98 APPENDIX. 

and B is greater than C, therefore a fortiori A is greater 
than C." The logical form is, 

Whatever is greater than a greater than C is greater than C ; 

A is greater than a greater than C, 

Therefore A is greater than C. 

Or if it be required that the a fortiori nature of the 
reasoning appear in the conclusion, we must state the 
major, " Whatever is greater than a greater than C is 
greater than C by a greater difference.'''' 

Of the same kind is the reasoning " A is equal to B, 
therefore twice A is equal to twice B." The logical 
form is, 

The doubles of equal things are equal ; 

Twice A and twice B are doubles of equal things, 

Therefore they are equal. 

The major premise might be stated more generally, 
" Equimultiples of equal things are equal." 



APPENDIX. 199 



Note E. 
is the syllogism a petitio principii ? 

The eagle of the Libyan fable was killed by an arrow 
feathered from his own wing. The armoury of the 
Logician has been fondly imagined to contain the fatal 
weapon of his own destruction. But the champion 
destined to wield it, if such there be, is somewhat tardy 
in his forthcoming. More than one Sir Kay has essayed 
the adventure of the sword ; the Arthur destined to 
achieve it remains in all the mysterious dignity of a 
Coming Man. In other words, many waiters have suc- 
ceeded in shewing their own ignorance of the nature of 
the fallacy called Petitio Principii"; they have not been 
equally successful in proving the invalidity of the 
Syllogistic process. 

Let us first endeavour to ascertain what the Petitio 
Principii really is. The name is a blundering trans- 
lation of the Aristotelian to Iv oigxV (*^^' "^^ ^^ *§'X^0 
aWsla-Qai : i. e. the assumption, not of the principle properly 
so called^, but, in some form or other, of the question 
originally proposed for proof. And it is remarkable, that 
among the five modes of this fallacy enumerated by 

" Of the numerous absurdities gravely propounded by Logicians in 
relation to this fallacy, perhaps the happiest is the exquisite etymology of 
Du Marsais, Logique, p. 81. " Ce mot s'aiDpelle petition de principe, du mot, 
grec ireTOfiai, qui signijfie volervers quelque chose, et du mot latin principinm, 
qui veut dire commencement; ainsi faire une petition de pinncipe, c'est 
recourir en d'autres termes a la meme chose que ce qui a d'abord ete mis 
en question." 

^ "■ Without entering on the vai'ious meanings of the term Principle, 
which Aristotle defines, in general, that from which any thing exists, is 
produced, or is known, it is sufficient to say, that it is always used for that 
on which something else depends ; and thus both for an original luu\ and 
for an original element." Sir W. Hamilton, Reid's Works, p. 76 L Cf. 
Arist. Metaph. IV. 1. •}. 



200 APPENDIX. 

Aristotle, one is in form not distinguishable from the 
legitimate Syllogism *=. Selecting this variety, as that by 
which most of all the objection is to be sustained, we 
will proceed to examine its peculiarities. 

In .the first place, it is manifestly necessary to a 
Petitio Quissiti^, as the fallacy may more correctly be 
called, that there should be a question proposed for 
proof. And hence it was long ago acutely remarked by 
Petrus Hispanus, that such a fallacy cannot be com- 
mitted in a Syllogism of inference^. If, that is, the ■ 
truth of the premises is known beforehand, and the only 
question is, what may we infer from them ? there is no 
necessity for begging or assumption of any kind. It is 
«lear then, that not the Syllogism in general, but at , 
most only one particular application of it, can beg the ' 
question. 

But it nmy be answered, that the truth of such premises 
never can be ascertained, but by a previous induction 
embracing all particular cases, and that Syllogistic in- 
ference is therefore at least futile, since the conclusion 
drawn must be presumed to be already known. But 
this answer itself assumes what has never yet been 
satisfactorily proved, the dependence of all knowledge 
of Universals on Induction. If axiomatic principles can 
be acquired in any other way, one class of Syllogisms 
at least exempt from the charged 



m / 
is I 



^ Top. "viii. 13.^. Aeurepov Se oTav Kara fxepos Se'ov OTroSeilai «a&oAou tis 
a'lT'fia'p, oTov iirix^ipcbv on rcov ivavriav fiio. eTTKTTTj/tTj, '6hws rwu ovt iK^Lfxivuv 
d|twcrete ixlav elvai. 

d Pacius in Anal. Prior, ii. 16. 

e " Sciendum quod hasc fallacia non impedit syllogismum inferentem, 
sed probantem, et ita fallacia pctitionis ])eccat contra syllogismum dialecticum 
in quantum dialecticus est." Summ. Log. Tract, vi. 

f Kant's criterion of necessity as the sui-e characteristic of a cognition 
a priori, has not yet been refuted by those who refer all principles to 
Induction. 



APPENDIX. 201 

And even with respect to principles allowed to be in- 
ductive, the actual previous assumption of every possible 
instance is not necessarily implied. And it is here that 
an able defender of the Syllogism, Mr. Mill, has taken a 
low and inadequate ground, a ground too, inconsistent 
with his own subsequent analysis of the process of 
Induction. His defence in fact amounts to an abandon- 
ing of all formal reasoning. All reasoning, he tells us, 
is really from particulars to particulars. But in that j 
case, all inference must depend upon the matter, and ^ 
cannot be reduced to any general type. If, for example, \ 
I conclude that a man now living is mortal, solely from j 
the premises, " A, B, and C, who are dead, were mortal, ( 
and this man resembles them in certain other attributes ) 
of humanity ;" I may, by an argument of precisely the 
same form, prove any given man to be six feet high, 
because A, B, and C, whom he resembles in the common 
attributes of humanity, were all of that stature. 

This portion of the question resolves itself into the 
following. What do we mean when we assert that all . 
men are mortal ? Is it merely a concise mode of stating \ 
that Socrates and Plato possess this attribute, in common ^ 
with a number of other individuals, quos nunc perscribere ) 
longum est ? If so, to argue, " Socrates is one of the I 
individuals above mentioned, therefore he is mortal," J 
is, if not a begging of the question, at least a needless 
repetition of a previous statement. 

But, in fact, the Uni versal Proposition m eans no_such 
things It means that, by virtue of a certain established 
law, certain attributes, or groups of attributes, are always ^ . 
so united, that in whatever individuals we find the one, 
we may look upon them as an infallible mark of the - ■ ' " '^ 
other. A conviction of this kind however, as it can ^ 
never be gained by any mere observation of particulars. 



C L 






c/vO^c^' 



tV^^i^<-^^ ^'f 




202 APPENDIX. 



^t -^ * ^^^ ^* need not presuppose a complete enumeration of 



c^i /- 



;^ - •- 



Uhem^. 



For, when one's proofs are aptly chosen, 
Four are as valid as four dozen." 



To determine under what conditions such a conviction 
can be obtained, is a question requiring the analysis of 
the whole process of Induction. Such an analysis, in 
many respects most ably performed^, will be found in the 
third book of Mr. Mill's Logic; but few I think can 
compare that part of the work with his earlier defence of 
the Syllogism, without admitting that the two presuppose 
diflferent and inconsistent theories of the import of 

% " Hinc jam patet, inductiouem per se nihil producere, ne certitudinem 
quidem moralem, sine adminiculo propositionum non ab inductione, sed 
ratione universali pendentium; nam si assent et adminicula ab inductione, 
indigerent novis adminiculis nee haberetur certitude moralis in infinitum. 
Sed certitude perfecta ab inductione sperari plane non potest, additis 
quibuscunque adminiculis, et propositionem banc : totum majus esse sua 
parte, sola inductione nunquam perfecte sciemus. Mox enim prodibit, qui 
negabit ob peculiarem quandam rationem in aliis nondum tentatis veram 
esse." Leibnitz, de Stylo NizoUi. 

Mr. Mill's adminicula to Induction are certain canons stating the prin- 
ciples of the Method of Agreement, of DiflFerence, &c. which, together with 
the whole law of universal causation, he makes dependent upon a weaker 
evidence than philosophical induction; the inductio per enumerationem 
simplicem. At the same time he enters his protest against " adducing, as 
evidence of the truth of a fact in external nature, any necessity which the 
human mind may be conceived to be imder of believing it." His words, 
strictly taken, would on his own shewing destroy the evidence of our 
senses ; for, according to the theory of perception adopted by himself and 
his favourite authority, Brown, sensations can only be regarded as states 
of mind, and the only reason we have for referring our internal conscious- 
ness to an external cause is, that by the constitution of our minds we are 
necessitated to do so. The admonition of Hooker is not quite obsolete 
even amid the lights of modern philosophy. " The main principles of 
Keason are in themselves apparent. For to make nothing evident of itself 
to man's understanding were to take away all possibility of knowing any 
thing. And herein that of Theophrastus is true, ' They that seek a reason 
of all things do utterly overthrow Reason.' " Eccl. Pol. i. 8. o. 

*» His theory of Causation must however be excepted. ^^ 










APPENDIX. 203 

Universal Propositions. It will be sufficient, however, for 
my present purpose to observe that, unless the establish- 
ment of an Universal Proposition requires an explicit^ 
and conscious examination of every existing and also of/ 
every possible particular instance, no charge of Petitio ) 
Principii, or even of vain repetition, can be maintained; 
against the Syllogism. Those who maintain the ante- I 
cedent, abandon themselves to an absolute scepticism*; I 
and against such, no defence of any source of humanJ 
knowledge can or need be attempted. ^ 

With regard to the syllogism of proof , we may examine 
the question a little more closely. The Petitio Principii 
is a material, not a formal fallacy, and consists in 
assuming, in demonstration, a non-axiomatic principle 
as axiomatic, or in dialectic disputation, a non-probable 
principle as probable ''. It does not affect the form of 
the reasoning; but depends on the selection of premises, 
when the syllogism is employed for the particular 
purpose of proof, demonstrative or dialectic. Those 
are guilty of it who do not adopt such premises as the 
laws of the two processes require ; in the one case, 
propositions axiomatic or deducible from axioms; in the 
other, probable statements, sanctioned by the general 
opinion of mankind or the authority of eminent persons. 

In reading Aristotle's account of this fallacy, it is 
evident that the whole point of the matter lies in the word 
aheia-Qoii, or Kaiju^uvsiv ; and that the question to be asked 
is, not whether the premises virtually contain the con- 

* Sed ea ratione prorsus evertuntur scientise, et Sceptic! vicere. Nam 
nunquam constitui possunt ea ratione propositiones perfecte universales ; 
quia inductione nunquam certus es, omnia individua a te tentata esse ; sed 
semper intra banc propositionem subsistes, omnia ilia, quae expertus sum, 
sunt talia; quum vera non possit esse ulla ratio universalis, semper 
manebit possibile, innumera, quae tu non sis expertus, esse diversa." 
Leibnitz, de Stylo Nizolii. 

t See Anal. Pr. ii. 16. Top. viii. 13. 



204 APPENDIX. 

elusion^, but whether such premises can properly be said 
to be heggedy or assumed"^. It is clear then that Petitio 
Principii is not the fault with which the Syllogism is 
chargeable, unless it can be shewn that every statement 
of an Universal Proposition must be, in this sense of the 
term, begging or assuming. If there are any cases in 
which the assertion of such propositions depends on 
a warranted conviction, not on a gratuitous assumption, 
from whatever source that conviction may arise, such 
cases must be exempt from the charge of Petitio 
Princijoii. 

And if there be any such cases, the opponents of the 
Syllogism have themselves unwittingly stumbled upon 
a fallacy cognate to that with which they taunt its 

^ One class of reasonings are perhaps fairly chargeable with the fallacy. 
I allude to what are commonly called the ■proper syllogisms of the Eamists, 
which have two Singular Premises. In the first figure, it is evident that 
the conclusion is not one out of many inferences contained in the major 
premise, but the very same proposition stated in difierent language. The 
third figure is open to the same objection, but it may be allowed as an 
€K0e(ris or expository instance — a process not reckoned by Aristotle as 
syllogistic. Proper syllogisms in the second figm-e are valid, and frequently 
serviceable ; but when reduced to the first, (which Aristotle regards as a 
necessary test of vahdity,) the negative premise must be converted from 
singular to universal. 

Nevertheless, as the Petitio Principii is a material, not a logical, fallacy, 
this does not furnish grounds for objecting to the convenient arrangement 
by which singular propositions are considered as in syllogism equivalent 
to universals. They may be regarded, in common v\dth other cases of the 
same fallacy, as reasonings valid in form^ but unsound from material 
circumstances. 

The Proper Syllogisms, however, though a post-AristoteUan innovation, 
did not originate with Eamus. Aquinas expressly denies that both premises 
in a syllogism may be singular, and admits the eKOeais as a non-syllogistic 
process, being an appeal to the senses, not to the reason. See Opusc. xixil. 
init. Occam, on the other hand, virtually surrenders the whole principle, 
when he allows that the major premise in the first figure may be singular. 
Logic, p. iii. cap. 8. 

•n That axiomatic principles are not of this character, may be seen from 
Anal. Post. i. JO. 6. Ou/c ecrTi 5' virSOeais ou8' atrTj/xa, t aydyKr] elvai S^^Mmh 
Koi doKeiv at/dyKT}. 



APPENDIX. 205 

defenders. For the Petitio Principii being in that case 
a particular misapplication of the syllogistic method, and 
postulating the latter as a condition of its practicability, 
they have inverted the relation of prior and posterior, and 
assumed Petitio Principii to be necessary to the existence 
of Syllogism. 

But if, on the other hand, there are no such cases, 
and the Syllogism is in consequence henceforth to be 
banished from Philosophy, what do we gain in ex- 
change ? We reduce the Laws of Thought from neces- 
sary to contingent. We degrade certainty into proba- 
bility, and can claim for that only a subjective validity. 
But until this latter hypothesis is proved, the Syllogism, 
whatever may be its errors or deficiencies, cannot be 
comprehended under any one of the fallacies admitted 
to he such hy the Logician. And this is sufficient as a 
defence of his own consistency. His method may be an 
incorrect analysis of the laws of the reasoning process; it 
may be that there are no such laws at all. But of either 
of these positions the onus prohandi lies with the assail- 
ants, not with the defenders of the Syllogism". It is quite 
enough for the Logician, if he exhibit all that is generally 
considered valid reasoning in a syllogistic form. If any 
maintain that a simpler or better type is attainable, he 
waits with patience till they produce it. If all reasoning 
is fallacious, he may be contented to behold his theories 
fall in the general overthrow of all human knowledge. 
But, pending the decision of this question, he may leave 



" To the charge of Petitio Principii which Campbell makes against the 
Syllogism, Archbishop Whately rephes, that it lies a(jainst all arguments 
whatever; the Syllogism not being a distinct kind of argument, but any 
argument whatever, stated regularly and at fuU length. And this reply is 
substantially vahd, even if we reject the Archbishop's mode of exhibiting 
Induction as a Syllogism in Bai'bara. For the objection of Campbell, if 
vaUd at all, lies against all formal reasoning ; and logical Induction, in its 
true analysis, is equally formal with the Syllogism. 



206 APPENDIX. 

his adversaries their choice of one or the other horn of a 
dilemma. If there are universal principles of truth not 
entirely dependent on sensation, the existence of such 
principles will warrant syllogistic inference. If there are 
not, whatever be the value of our individual sensations, 
all inference from them, by induction, example, analogy, 
or any method whatever, is, in respect of objective 
certainty, worthless. 



APPENDIX. 207 



Note F. 
on the enthymeme. 

The Enthynieme is defined by Aristotle, (7vX\oyi(T[Ms 
\oitsKyi{\ ^f slxoTODv vj <rYiiji.siMv. The word otTsKyjs is now 
universally admitted to be spurious; and that upon 
abundantly sufficient evidence, both external and in- 
ternals Externally, it is not countenanced by the best 
MSS. Internally, it is inconsistent with the ordinary 
language of Aristotle ; with whom the imperfect syllogism 
signifies, not a Syllogism with one portion suppressed, 
but a Syllogism in the second or third figure, which is 
not immediately evident by the dictum de omni et nulla. 
The word is an interpolation, and a clumsy one, designed 
to accommodate Aristotle's definition to subsequent views 
of the nature of the Enthymeme, and made by a scribe 
not particularly well versed in Aristotelian phraseology. 

The elxof and <r>)ju.£<ov themselves are Propositions''; the 
former stating a general prohahility^ the latter a fact, 
which is known to be an indication, more or less certain, 
of the truth of some further statement, whether of a single 
fact or of a general belief. The former is a proposition 
nearly, though not quite, universal; as, " Most men who 



* For a full account of the evidence on this point, see Pacius on Anal. 
Pr. ii." 27. 3. and Sir W. HamUton, in Ed. Rev. No. 115. p. 222. 

*» As is stated, Anal. Pr. ii. 27. 1. and Rhet. i. 3. 7. In a looser sense, 
however, the terms ^kSs, (Ti/]^ilov, reKfi-fipiov, are often used for the Enthy- 
memes drawn from each. The elnhs is clearly regarded by Aristotle as a 
general proposition, employed as a premise. In the Rhetoric, i. 2. 15. he 
describes it as having the same relation to its conclusion as an universal 
to a particular. In another sense, any proposition may be called probable, 
which can as a conclusion be supported upon (moraUy) reasonable grounds; 
in which sense Anaximenes, or whoever was the Author of the Rhetorica 
ad Alexandrum, defines the ei/ctJy. (ch. 8. 4.) 



•208 APPENDIX. 

envy hate :" the latter is a singular Proposition, which 
however is not regarded as a sign, except relatively to 
some other Proposition, which it is supposed may be 
inferred from it. The elxoV, when employed in an Enthy- 
meme, will form the major premise of a Syllogism such 
as the following : 

Most men who envy hate^ 
This man envies, 
Therefore, This man (probably) hates. 

The reasoning is logically faulty ; for, the major premise 
not being absolutely universal, the middle term is not 
distributed. 

The o-yjju-sTov will form one premise of a syllogism which 
may be in any of the three figures, as in the following 
examples : 

Fig. 2. 



Fig. 1. 



All ambitious men are liberal; 
Pittacus is ambitious (s), 
Therefore, Pittacus is liberal, 



All pregnant women are pale. 
This woman is pale (2), 
Therefore, She is pregnant. 



Fig. 3. 
Pittacus is good (s)% 
Pittacus is wise, 
Therefore, All wise men are good. 

c In the first and second figures, the a-rjixelov is cleai'ly the mmm- 
premise ; this alone heing singular. In the third, as far as quantity is 
concerned, we may choose hetween both premises. It seems more natiu-al 
however to prefer the major; because, in assigning a reason for om- belief 
in a given proposition, we should naturally state a premise having either 
the same predicate or the same subject; not one in which the predicate of 
the premise is the subject of the conclusion. For example : Why do you 
believe Pittacus to be liberal ? Because he is ambitious. "Why do you 
believe wise men to be good ? Because Pittacus is good. This is far more 
natural than to answer, " Because Pittacus is wise." The same consideration 
will furnish the data for interpreting an obscm-e passage in Anal. Pr. ii. 26. 
5. which however it would exceed my present limits to attempt. The reader 
will find it rightly explained in a note to St. Hilaire's Translation^ vol. ii. 
p. 341 . with the exception that the syllogism may be more clearly stated in 
Cesare than in Camestres. 



APPENDIX. 200 

The S^yllogism in the first figure is alone logically valid. 
In the second, there is an undistributed middle term : in 
the third, an illicit process of the minor. 

The cr>j/^eIov is defined by Aristotle, Tr^oracrjj uTrohiKTixr}. 
StmyKulu Yi evdo^o$ ; in which the words necessary and 
probable do not relate to the modal character of the 
Proposition in itself, but to the nature of its connexion 
with the Conclusion which it is adduced to prove j i. e. to 
its logical validity when the other premise is added "^ ; 
without which addition, expressed or understood, there is 
no Enthymeme at all^. 

But it may be thought that the above examples- do not 
furnish a sufficient criterion for distinguishing between 
the two kinds of Enthymeme. If both premises must he 
mentally, and may be orally, supplied, before there is 
any Enthymeme at all, how are we to determine whether 
any given specimen is an instance of reasoning from a 
sign, or from a likelihood ? Why, for example, in the 



^ Rhet. i. 2. 17. ^Pi.vayKa7a fieu oZv Xcyo} 4^ wv yiperai (Tvk\oyi(rix6s. Cf. 
Anal. Pr. i. 1. 6. SwAAoyto'/xbs Se iari \6yos iu ^ reOevTcau rivwv erepSv Ti 
ruv Keifieuwu e| au ay Kr}s aufi^aluei. Here sylloyism is used iu its strictest 
sense. From another passage in the Rhetoric (i. 2. 14.) it has sometimes 
been imagined that all a-rjixela are necessary, at least as propositions ; and 
the crrjiJLelov has even been defined, " a proposition in necessary matter ;" 
as if " necessary matter" were the proper province of Rhetoric. Tlie inter- 
pretation however is too inconsistent with Aristotle's subsequent language 
to be tenable. The words in question, if properly belonging to this place, 
(the res.emblance to Rhet. i. 2. 8. is suspicious,) must be so interpreted as 
to identify the necessary propositions with one class only of arffiela, the 
reKfi-fipia. The reference to the Analytics I conceive to allude, not to the 
account of modal conclusions deduced from modal premises, but to the 
necessary conclusiveness of premises logically connected, as opposed to the 
more or less probable conclusiveness of illogical combinations. As a special 
reference, supply Anal. Pr. i. 27. 12. 

^ Anal. Pr. ii. 27. 4. ^Ehv /iey ovv rj /xia Aex^p irpSraais, arifieloy yiverat 
fiSvov, iau Se ko.) rj cTepa Trpoa\rj<p9f}, avWoyi(TiJ,6s. The context shews that 
he is speaking of Syllogism only in the looser sense in which all Enthy- 
memes are included. 



210 APPENDIX. 

instance given above, may we not call the fact that " this 
man envies," a sign that he hates, as well as the general 
statement a likelihood? Does not the whole distinction 
depend on the question, which is the stated, which the 
suppressed, premise ? 

To this it may be replied, that Aristotle distinguishes 
the sWog and o->5|U,e7ov merely as propositions, and no where 
says that they may not be combined in the same syllogism. 
In the instance given, it so happens that the minor premise 
is a singular proposition, and may fairly be considered a 
sign of the conclusion. But we might obviously employ 
a minor premise of another kind, such as, " All malig- 
nant men are envious ;" in which case there is, properly 
speaking, no sign employed in the reasoning. But this 
does not aifect the distinction between the two Pro- 
positions. A likelihood is such, per se, — a proposition 
stating a general truth, which w^e are at liberty to apply 
or not to particular cases. A sign is a sign of something 
else, — a single fact stated as a proof of something further; 
which proof may, according to material circumstances, be 
logically or only morally conclusive. 

Another question sometimes raised is, " If the En- 
thymeme has both premises supplied, how is it to be 
distinguished from the Dialectic Syllogism .?" To which 
it may be answered, that, taking the word Syllogism in 
its strictest sense, as a reasoning logically correct, the 
same argument may in different points of view be con- 
sidered either as a Syllogism or an Enthymeme. This 
is, of course, only the case w4th the Tsxfx^giov; the other 
specimens of the Enthymeme being logically invalid. 
The argumentation Ix Tsx.[xriglot} is in this sense both 
an Enthymeme and a Syllogism ; — an Enthymeme on 
material grounds, inasmuch as its premise is a sign 
of its conclusion ; — a Syllogism on formal grounds^, 
inasmuch as it complies with the conditions of logical! 



APPENDIX. 211 

reasoning. It is a Dialectic Syllogism, if employed for 
the purpose of dialectic disputation ; and, as it usually 
relates to those subjects to which dialectic disputation is 
practically applied^, it may in general be regarded as, 
potentially at least, dialectic*. 

In fact, it is not as an Enthymeme, but as a Rhetorical 
Syllogism, that a given specimen of reasoning is dis- 
tinguished from the Dialectical. The object of the two 
arts is distinct. That of Dialectic is to convince the 
Intellect; that of Rhetoric, to persuade the Will. The 
same instrument may be employed by both, and it is 
merely the purpose for which it is employed that con- 
stitutes the distinction between them^. Whether the 
same means are always available for both purposes ; 
whether the same informality of reasoning is allowed in 
Dialectic as in Rhetoric, must depend on the conditions by 
which the disputants in the former choose to bind them- 
selves. The Rhetorician has to influence an audience: if 
he can effect this, he will not always be scrupulous about 



^ This, however, is by no means necessary. Matters not usually discussed 
either by the Dialectician or Orator may equally be proved by means of 
rcKfi-fipia. For example ; the falling of the thermometer to '32° is a sign of 
freezing ; the obscuration of the moon in eclipse is a sign that the earth's 
shadow is interposed between it and the sun. Such subjects are not 
practically dialectical, at least in Aristotle's view of the art. As far as 
the mere interrogatory form is concerned, it may be, and was by different 
Philosophers, applied to all varieties of matter. 

s This proceeds on the supposition that the Dialectician is bound to 
logical accuracy in his reasonings ; a restriction which Aristotle at least 
would regard as salutary. See Anal. Post. i. 6. 10. We need not however 
suppose that all disputants actually conformed to it. 

^ Cf. Crakanthorpe, Logic, lib. v. cap. 1. " Utiique Disciplinge hoc com- 
mune est, quod doceat probabiliter arguere : finem vero diversum uterque 
sibi proponit. Quoniam ergo eadem omnino forma probabiliter arguendi 
uterque utitur, nos hie quod utrisque commune est tractabimus, unicuique 
liberum rehnquentes, an Dialecticus esse velit, et uti hac forma proba- 
biliter arguendi ad verum inveniendum ; an Rhetor, et uti eadem forma 
probabiliter arguendi ad suadendnm aut dissuade ndum." 

p 2 



212 APPENDIX. 

the logical accuracy of his reasoning. In Dialectic, two 
champions are opposed to each other: they may, before 
engaging, dictate the conditions of the combat. 

As regards the account of the Enthymeme in the 
Prior Analytics, I am not aware that any further expla- 
nation is needed^ But in the corresponding chapters of 
the Rhetoric one or two difficulties remain, an elucida- 
tion of which, though not strictly within my present 
province, may perhaps be serviceable to the readers of 
the latter Treatise. 

In Rhet. i. 2, 18. we are told, that when the Enthymeme 
is in the third figure, the (rrifji,slov is to its conclusion as a 
particular to an universal. In the second figure, on the 
other hand, as an universal to a particular. The relation 
in the first figure is not mentioned, but the context seems 
rather to connect it with the former than with the latter. 

This passage may be interpreted in two ways. Either 
we may compare the conclusion of the Enthymeme 
with the G'rjfteTov itself, or with the major premise of 
that Syllogism whose minor is the (TYifxmv. In the former 
interpretation the word (tyi^sIov is used properly for the 
proposition; in the latter widely, for the reasoning of 
which such proposition forms a portion. 

If the first interpretation be adopted, (which seems 
preferable,) we must compare the two propositions 
relatively to that term in which they are unlike ; i. e. if 
they have the same subject, we must compare their 



> Except perhaps that Aristotle, in Anal. Pr. ii. 27., admits a (rrjfieiou in 
the second figure, Avhich in the former chapter he condemned. The con- 
demnation seems to be made on logical groimds. The logical value of two 
afl&rmative premises in the second figure is absolute zero; whereas the 
ff-nuelov in the third figure, though faulty as employed to prove an universal 
conclusion, is valid for particulars. For rhetorical purposes, however, the 
second figure is also admissible ; an accumulation of Enthymemes, all 
logically worthless, may amount to a moral certainty. 



APPENDIX. 213 

predicates; if they have the same predicate, we must 
compare their subjects. 

According to this method, it will be seen, that in the 
first figure, the predicate of the sign is to that of its 
conclusion as part to whole, or as species to genus. 
Hence its logical validity : whatever subject is included 
under a species is necessarily included under its genus. 
But in the second figure the relation is that of whole to 
part, or of genus to species ; and this is illogical, the 
whole genus not being included under one of its species. 

But if we adopt the second interpretation, and compare 
the major premise with the conclusion, we shall be com- 
pelled in the first figure to compare together the two 
subjects, since both propositions have the same predicate. 
In this case the relation will be inverted ; the premise 
being to the conclusion as an universal rule to a single 
instance. In the second figure, we are at liberty to 
compare either the quantity of the two propositions as 
determined by their subjects, or the extent of their 
respective predicates. In either case, however, the result 
is the same ; the relation remaining that of universal to 
particular. 

The Enthymeme in the third figure presents no diffi- 
culty. Whichever interpretation be adopted, the same 
proposition, "Pittacus is good," is compared with the 
conclusion, " All wise men are good." In both cases, 
the comparison lies between the two subjects, and the 
relation is that of particular to universal. 

But perhaps the most difficult passage in this portion 
of the Rhetoric is that in which Aristotle describes an 
important, and previously, as he tells us, unnoticed 
distinction between various classes of Enthymemes. 
Some of these, he says, belong to Rhetoric, some to 
other arts and faculties. The same may be said of the 
connexion of the Syllogism with Dialectic. Dialectical 



214 APPENDIX. 

or Rhetorical reasonings are founded on toVoi ; the 
others on the peculiar principles of that Science or Art 
to which they belong^. 

This passage is generally found puzzling to a beginner 
on two accounts. Firstly, he is apt to fancy Dialectic 
synonymous with Logic, and to confound it with the 
formal Science of that name ; an error which the Com- 
mentary most likely to fall in his way is not unlikely 
to confirm. Secondly, having previously seen the Enthy- 
meme defined as the Rhetorical Syllogism ; there seems 
some inconsistency in the subsequent observation, that 
some Enthymemes are Rhetorical, others not so. 

In explanation it may be observed. Firstly, that 

Dialectic and Rhetoric are not formal Sciences, but 

material Arts. Their Logic is not a Logica docens, 

treating of the general form of Reasoning, but a Logica 

uteris, treating of Reasoning as applied to a particular 

matter. That matter is furnished by the T6'7:Q^. Rhetoric 

and Dialectic do not merely lay down the form in which 

their reasonings ought to proceed, but likewise provide 

certain general principles of probability, from which the 

matter of their major premises is to be drawn. These 

TOTTOi or common-places hold the same position in the 

Dialectic Syllogism, as the most universal kind of 

axioms in the Demonstrative. They are not gained by 

exclusive observation of any one particular class of 

objects belonging to this or that art or faculty, but are 

indifferently applicable to all. Such is the example 

quoted by Aristotle as 6 rot) jOtaAAov jca) ^ttov tottoj. Of 

this in the Topics he gives four cases, of which the 

following may be taken as a specimen. "If the more 

likely assertion on any subject be untrue, the less likely 

is probably untrue likewise." A general maxim of this 

k Rhet. i. 2. 20, 21. 



APPENDIX. 215 

kind is obviously available '^rsg) dixottoov xa) (^v(nxa>v Koti Trsgl 

Secondly, it may be observed that the Enthymeme is 
not necessarily confined to the Rhetorical kind of matter. 
A syllogism from likelihoods or signs, whatever be the 
object, is an Enthymeme. In like manner, any syl- 
logism in probable matter may become an instrument of 
Dialectic reasoning ; whether it be based on the general 
probabilities which Dialectic materially furnishes, or on 
more limited assumptions drawn from special observ- 
ations. The Physician, for example, within the field of 
his own experience, may know that in nine cases out 
of ten where a patient exhibits certain symptoms, the 
disease terminates fatally. The student of history may 
learn that in the majority of cases revolution leads to 
anarchy, and anarchy is suppressed by despotism. Either 
of these may become the basis of a reasoning process 
in probable matter ; but the Syllogism or Enthymeme is 
not, properly speaking. Dialectical or Rhetorical, but 
Medical or Political. And although there is nothing in 
the Dialectical or Rhetorical Method that prevents its 
being applied to these or any other special subjects, yet 
in proportion as any one so applies it, Aristotle regards 
him as departing from the legitimate matter of Dialectic 
or Rhetoric, and adopting that of some definite Art or 
Science ^ For the same reason, when he speaks of the 
special application of Rhetoric to Political deliberation, 
he warns us that its object matter must not be consi- 
dered as that of Rhetoric p'er se, but as primarily and 
properly belonging to Politics, secondarily only to 
Rhetoric in one of its practical applications'". 

^ Rhet. i. 2. 21. Tavra Se, '6o-C() tis ttu fi4\Tiov iKKeyrjTai ras irpoTcicreis, 
Kifcrei TTOiijaas &\\7}v iiriarrjfMTjv ttjs 5toAe/cTi/c7]s koI pT)T0piK7Js' hu yap iuTvxri 
apxcus, ovk4ti SiaKeKTiK^ ovBe pT}T0piK7f a\\' iKeivrj iffrai ^s exet Toy apx^s, 

« Rhet. i. 4. 4, 5. 



216 APPENDIX. 

A few words in conclusion on the origin of the name 
Enthymeme. That its etymology is to be found in Iv 
and Qu[ji.05, is undeniable; but only in the same degree as 
is also true of svSujxsTcrSa*, sv$v[jnog, and other cognate terms. 
But that it has no special reference to a premise in the 
mind, is evident; firstly, because $u[juo; in the Aristotelian 
phraseology is not " the mind," and has nothing to do 
with the expression or suppression of premises: secondly, 
because the word evQuixru^ot occurs in writers earlier than 
Aristotle, and before it could have assumed its technical 
meaning. To ascertain the true derivation, however, is 
not so easy as to refute a palpably absurd one. If, 
however, we were compelled to make a suggestion, the 
following, though not confidently put forward, has at 
least the merit of not being positively ridiculous. Ac- 
cording to the analogy of words of the same termination, 
such as <p/Aocro'<^»jjxa, e7ri^slgr}[ji.ot, <t6(Pkti/.u, &C. ev$6ix,YjiJi,o(. will 
properly signify the result of an act of reflection". Hence 
it is used by Sophocles for a thought suggested by a person 
or thing", and by Xenophon? for di,plan designed, opposed 
to iqyov, the execution. The term is thus naturally enough 
applicable to the suggestions or persuasive arguments of 
Rhetoric, as distinguished from the demonstrations of 
Science. 



^ Cf- Melanchthon, Erotem. Dial, p, 187. Enthymema significat cogita- 
tionem seu quiddam cogitatum, ut nos dicimus, Ein Bedenken. 
o (Ed. Col. 292, 1199. 
P Anah. iii. 5. 12. See also (Econ. 20. 24, 



APPENDIX. -^ 217 



Note G. 
on induction. 



Induction, as far as it is a Logical process at all, is 
equally formal with Syllogism ; though proceeding in 
the inverse order; viz. from the aggregate of individuals 
to the universal whole constituted by them ; instead of 
from the whole to the several individuals contained^ 
under it. It is defined by Aristotle, " proving the 
major term of the middle by means of the minor";" 
in which definition, the expressions major, middle, and 
minor, are used relatively to their extension, to designate 
respectively the attribute proved, the constituted species 
of which it is proved, and the aggregate of individuals 
by which the species is constituted. The form in which 
the Inductive Reasoning'* naturally appears, exhibits an 
apparent, though not a real, resemblance to the third 
figure of Syllogism. Thus : 

X, Y, Z, (minor,) are B (major); 

X, Y, Z, are all A (middle) ; therefore, 

All A is B. 

The resemblance to the third figure is apparent only; 
the true distinctions being, 1. That in the minor premise 
of the Induction, the copula does not represent the 
subject as contained under, but as constituting, the 
predicate. 2. That in consequence of this distinction, 

'^ Th Sict Tov erepou ddrepov &Kpov rcfi fieffcfi avKKoyiaaaBai. Anal. Pr. ii. 
23.2. 

•» In a loose sense, Aristotle calls it o e| iirayuyris av\Koyi(Tix6s, where 
the word does not denote the syllogism proper, or reasoning from the 
universal whole to the contained parts, but is extended to formal reasoning 
in general. In like manner, in Rhet. ii. 25. 8. he speaks of the Enthymeme 
as including Example, 



218 APPENDIX. 

an universal conclusion is logically drawn in this form, 
which is not valid in the third figure of Syllogism. 

We see then, that in the Inductive process the Copula 
is ambiguous, expressing in the major premise and in 
the conclusion, the relation of a contained part to a 
containing whole ; in the minor premise, that of consti- 
tuting parts to a constituted whole. This ambiguity has 
been remarked as a deficiency in technical language *"; 
but there is no term sufficiently naturalized in Logic to 
serve as a substitute to express the latter relation. 

On Induction, as exhibited above, it may be remarked, 

I. That the distinction between a perfect and an im- 
perfect Induction is extralogical. Logic recognises no 
inference that is not necessitated by the Laws of Thought: 
and therefore it must be presumed that the Induction is 
perfect, i. e. that the Individuals mentioned are in reality 
the whole constituents of the species, before the In- 
ductive Inference can come in any way within the 
province of the Logician. To inquire what is the 
warrant for this presumption ; to ask what amount of 
observation will warrant us in assuming X, Y, and Z, to 
be all the members of the class A; is like asking in 
syllogistic reasoning, how do we know that the premises 
are true ? undoubtedly a most important question, but 
not to be answered by Logic. So also any compromise 
with material probability, any statement of the indi- 
viduals as samples or adequate representatives of their 
class '^, is a surrender of the essential principle of 
Logical Reasoning : the parts are absolutely the whole ; 
or the inference is, logically speaking, worthless. 

It is manifest, however, that the Induction may be 
easily stated in such a form, as to transfer the material 

<= Edinburgh Review, No. 115. p. 229. From this admirable Article the 
greater part of the materials for the present note have been derived, 
d Whately's Logic, p. 260. (Sixth Edition.) 



APPENDIX. 219 

difficulty from the minor premise to the major; in which 
case the question may be satisfactorily answered by that 
Art or Science to which the Proposition materially 
belongs. Thus the example given by Aldrich might be 
stated as follows : 

The magnets which I have observed, and also those which 

I have not observed, attract iron ; 
The magnets which I have observed, and those which I have 

not observed, are all magnets ; 
Therefore, All magnets attract iron. 

In this mode of stating, the minor premise is unde- 
niably true. The doubtful part of the major, relating to 
the properties of unobserved objects, must be determined 
by the analogies of the Science to which the objects 
belong, and by the material inquiry, what kind of 
samples or specimens will warrant our asserting of 
others what we have observed in them. 

II. It is precisely in the mode of answering this 
material inquiry, that the whole difference lies between 
the ancient Inductio per enumerationem simplicem, and 
that Interpretation of Nature insisted upon by Bacon. 
The disciple of the former method, when asked. How do 
you know that other specimens of your class possess the., 
same property as these } will reply. Because I have 
never seen one which does not possess it. The Ba- 
conian, on the other hand, will answer. Because I have 
selected such instances as give evidence of an universal 
law : I have examined those specimens of the class 
which have nothing in common, except the possession 
of the property in question : I have compared them with 
objects not possessing it, and I find its absence always 
accompanied by that of one of the essential attributes 
of this class ^ 

« Bacon, Nov. Org. lib. ii. Aph. x sqq. xxii sqq. 



220 APPENDIX. 

A recent writer has exhibited the Inductive Method of 
Socrates as a specimen of that Inductio per enumera- 
tionem simplicem which the Baconian philosophy has 
superseded^ But it has been before observed that the 
Socratic reasoning is not properly Induction, but Example, 
It is inconclusive, not because it is an Induction by 
Simple Enumeration, but because it is no Induction at 
all. The Simple Enumeration, if complete, will form the 
basis of what, logically speaking, is a valid Induction; 
and it is precisely because the Socratic Method does 
not pretend to completeness, that Logic does not recog- 
nise the inference. It is true that in Simple Enumeration 
this completeness is often difficult, sometimes impossible 
to attain. And it is the additional security on this point 
that constitutes the chief merit of the Baconian process. 
But this is a material, not a logical, merit. It affects our 
ground of confidence in the truth of certain propositions, 
not the nature of the inference from those propositions 
assumed to be true. Neither in Induction nor in Syl- 
logism does the Organon of Bacon supersede that of 
Aristotle. " Each," as Sir W. Hamilton observes, 
" proposes a different end; both, in different ways, are 
useful 8." The ancient Philosopher considers " the laws . 
under which the subject thinks;" the modern, "those; 
under which the object is to be known." The Induction] 
of Bacon, as furnishing more accurate rules for physical 
investigation, may supersede the Induction of Socrates ; 
for the latter owes its validity solely to the matter. It 
cannot affect the Induction of Aristotle, of which the 
validity depends solely on the form. 

The perversions of the Aristotelian Induction by Aldrich 
and Archbishop Whately have already been noticed. On 
this point it will be sufficient to observe, that any attempt 

f Lewes, Biographical History of Philosophy, vol. i. p. 215. 
g Reid's Works, p. 712. 



APPENDIX. 221 

j to reduce Induction to Syllogism, in the strict sense 
1 of the term, must commence by inverting the whole 
operation ; stating as a preliminary assumption that 
which is really the conclusion of the Inductive process. 
It moreover leaves us no alternative between converting 
mere empirical judgments into self-evident axioms, or 
destroying the whole foundation of reasoning, by com- 
mencing with a Syllogism whose premises themselves 
must be proved by another Syllogism, and so on ad 
infinitum. 

The Aristotelian Induction proper has been described 
as an analytical, its counterpart, Syllogism, as a syn- 
thetical process ; and the two have respectively been 
identified with the -^o^^oi I'ttj ra^ «gX^^ ^^^ ^"^^^ '^^'^ ^^X^^ 
of Aristotle •". And this is in one sense correct, though, 
according to a various notion of whole and part, the 
terms Analysis and Synthesis have perpetually been 
interchanged with each other. According as we look to 
the comprehension, or to the extension of the notions, we 
may regard the Genus as a part of the Species, or the 
Species as a part of the Genus. Hence the notions of 
Synthesis and Analysis, of the composition of parts into 
a whole, and the resolution of a whole into parts, will, 
as we adopt the one or the other point of view, be 
inverted. We have previously spoken of Induction as 
an inference from the constituting parts to the con- 
stituted whole. In this respect it is synthetical, the parts 
and whole being viewed in their logical or extensional 
relation. In the same point of view, the Platonic 
method of division is sometimes called analytical '\ On 
the other hand, in the ordinary modern use of the terms. 
Induction is analytical, adopting the metaphysical relation 
of part and whole as simpler or more complex notions. 

h See Michelet in Eth. Nic p. 25. 

i Diog. Laert. iii. 24. Van Heusde, Tnitia, p. 261. 



222 APPENDIX. 

In this point of view, Division and Definition are respec- 
tively the Synthesis and Analysis of notions as expressed 
in simple terms. In the former, we combine Genus and 
Differentia into Species; in the latter, we resolve Species 
into Genus and Differentia. A similar relation exists 
between the processes of uniting Accidents to a Species, 
in distinguishing its several individuals, and abstracting 
the Specific notion from the Accidents, in the formation 
of Universals. Syllogism and Induction in like manner 
are respectively the Synthesis and Analysis of the same 
notions when forming the subjects of a judgment. For 
on examination of the first figure, which is the natural 
form of Syllogism, it will be seen, that it proceeds, by 
division of the middle terra, to predicate of the several 
Species what was previously predicated of the Genus. 
Induction, on the other hand, in its natural form, pro- 
ceeds by a process of abstraction, from the individuals 
constituting a Species to their common Species so con- 
stituted. 

As regards the etymology of the name ; both the 
Greek eTrayooyv), and its Latin equivalent Inductio, seem 
to have been originally applied with reference to the 
Socratic accumulation of instances to serve as an ante- 
cedent for establishing the required conclusion. The 
Platonic use of sTrotysiv will support this view''. Such is 
also clearly the interpretation of Cicero. " Hoc in genere 
praecipiendum nobis videtur, primum, ut illud quod 
inducemus per similitudinem, ejusmodi sit, ut sit necesse 
concedi; nam ex quo postulabimus nobis illud quod 
dubium sit concedi, dubium esse idipsum non oportebit. 
Deinde illud cujus confirmandi causa fiet Inductio, viden- 

•' Cratyl. p. 420. d. Tavra ijdr] fj-oi So/ceTs, 5 Sc^Kpares, irvKpSrepov iirdyeiv. 
Where Heindorf renders, " Confertius quam priora afferre, ita ut alterum 
alteri addas, in singulis nihil immorans." The substantive iirayoiy^ has a 
very different sense in Plato; e. g. Eep. ii. p. 364. c. Leg. xi. 933. d. Cf. 
Ruhnken, Timseus. 



APPENDIX. 223 

dum est ut simile iis rebus sit, qiias res, quasi noD 
dubias, ante induxerimusK^'' Quintilian, however, applies 
the term rather to the bringing in, as an inference, of the 
question to be proved. " Nam ilia, qua plurimum 
Socrates est usus, banc habuit viam ; cum plura inter- 
rogasset, quae fateri adversario necesse esset, novissime id, 
de quo quaerebatur, inferebat, cui simile concessisset ; id 
est inductio™." Another meaning of the Greek e•7^ays^v 
and sTTocyooyog, as well as of the Latin inducere and in- 
ductio, might seem to point rather to the persuading and 
influencing the mind of the hearer °. But the first deriva- 
tion is preferable. The question, however, as far as 
Aristotle is concerned, is not of any great consequence. 
For, as that Philosopher did not invent the name, but 
only modified the usage of a term current among his 
predecessors, the etymology will be of little service 
towards illustrating the notion which he attached to it. 

1 De Tnventione, i. 32. 
™ Inst. Orat.v. 11. 

" Kod. Agric. de Inv. DiaLii. 18. Melanchth. Erot. Dial. p. 188. Bur- 
gerdsd. Inst. Log. ii. 11. 



224 APPENDIX. 



Note H. 
on example and analogy. 

Example is defined by Aristotle, " proving the major 
term of the middle by a term resembling the minor*." 
This definition is obscure, from being worded so as to 
contrast with his definition of Induction, in which the 
major term is proved of the middle by the minor. It 
does not apply to the singular conclusion ultimately 
established, but to the universal proposition which forms 
the conclusion of the inductive portion of the Example. 
Thus, if we expand Aristotle's instance into its complete 
form, composed of an imperfect induction and a syllo- 
gism, it will run thus : 

The war of the Thebans and Phocians (D) was an 

evil (A), 
The war of the Thebans and Phocians was a war between 
neighbours (B), 
.'. All wars between neighbours are evil. 

A war between the Athenians and Thebans (C) is a war 
between neighbours, 
.*. It is an evil. 

In this reasoning there are four terms, A the major, B the 
middle, C the minor, D the 6[ji.ohv. The definition applies 
to the third proposition, in which A is proved of B by 
means of D. If the final conclusion were taken into 
account, the Example might be more correctly defined 
as a reasoning in which the major term is proved of the 
minor by means of a middle, of which middle the major 
has been proved by a term resembling the minor. 

* Ilapddeiyixa 5' iarlv Brav t^ fxeacf rh &Kpov virdpxov Seix^^ Sia tov ofioiov 
rcf Tpir^. Anal. Pr. ii. 2i. 1. 



APPENDIX. 225 

Example differs from Induction in two principal 
points. I. Induction enumerates all the individuals 
in the minor term, so as to constitute the middle : Ex- 
ample selects single instances. 2. Induction stops at 
the universal conclusion : Example proceeds to infer 
syllogistically a conclusion concerning another indi- 
viduaP. 

The Example, as thus exhibited, has no logical value 
as an independent reasoning. We are not warranted in 
assuming, as a necessary law of thought, that two things 
which resemble each other in any one given quality must 
likewise resemble each other in any other". The reason- 
ing may have more or less material weight, according 
to the character of the particular qualities compared, 
and to what we may empirically know of their connection 
with each other. It thus comes under the kind of 
evidence mentioned by Bishop Butler^ as probable; 
which admits of degrees, and of all variety of them, 
from the highest moral certainty to the very lowest 
presumption. But degrees of evidence are inadmissible 
in Pure Logic. Either the conclusion necessarily 
follows from the admitted truth of the premises, or it 
does not. In the former case, all reasonings are in a 
logical point of view equally necessary ; in the latter, all 
are equally worthless ^ That the inference in Example 
is material, not formal, appears the instant we attempt 
to state it in symbolical form : e. g. A and B are both 
X, A is also Y, therefore B is Y. This reasoning has no 
force until we know the ^natter, i. e. what particular 
objects are signified by A and B, X and Y^ 

*" Anal. Pr. ii. 24. 3. 
« Cf. Hegel, Werke, vol. v. p. 151. 
^ Introduction to the Analogy. 

e See Sir William Hamilton, Edinburgh Review, No. 115. p. 225. 
^ Kant classes imperfect induction and analogy as syllogisms of the judg- 
ment, diaA. describes them as furnishing a logical presumption of their con- 



226 APPENDIX. 

On the other hand, the Example has a strictly logical 
value, when it is used, not as an independent reasoning, 
but as an answer to objections. Thus it does not logically 
follow, because A and B are both X, and A is Y, that B is 
also Y. But the union of X and Y in the instance of A 
logically proves that X and Y are not incompatible with 
each other ; that one X at least is Y; and therefore that the 
two attributes may coexist in the same subject. Hence 
the Example is logically valid against any reasoner who 
maintains that a thing cannot be Y, because it is X. But, 
in this case, the conclusion is not assertorial, " B is Y," 
but only problematical, '' B may he Y." 

The Example is sometimes loosely called reasoning 
from Analogy^. This term however, properly belongs, 
not to absolute similarity in any given quality, but only 
to similarity of relations. Thus Aristotle speaks of an 
analogy between sight and intellect, the one being re- 
lated to the body as the other to the souP\ And the 
argument of Bishop Butler's Analogy of Religion to the 
Constitution and Course of Nature may be put into the 
same form. The difficulties in Religion, natural and 
revealed, have the same relation to their respective 
systems, that the difficulties in the course of nature have 
to the entire system of nature. If then the latter be 
admitted to proceed from a Divine Author, the diffi- 
culties in the two former are not a valid objection 
against a like origin. This reasoning from Analogy 
corresponds to what is sometimes called the Induc- 
tion of Socrates, and to the TragufSoXy] mentioned in 
Aristotle's Rhetoric \ Like the Example proper, it 

elusion. But this classification ought to have excluded them from Formal 
Logic. 

8 See Reid, Intellectual Powers, i. 4. 'Mill, Logic, b. iii. ch. 20. Hoff- 
bauer, Logik, §. 453. Krug, Logik, §. 168. 

h Eth. Nic. i. 4. 12. Cf. Whately's Rhetoric, Appendix, note E. 

* Uapa^oX^ Se rh 'ZuKpaTiKo.. Rhet. ii. 20. 4. Compare the reasoning of 



APPENDIX. 227 

has no logical value as an independent reasoning; its 
symbolical form being, A is to B as C to D ; A is X, 
therefore C is X. Here it is evident that the premises 
may be true and yet the conclusion false. Its material 
value, like that of Example, may admit of any degree, 
from zero to moral certainty. Like Example too*, it 
has a logical value as an answer to objections. Thus, 
in Butler's argument, the difficulties in Religion are 
not intended logically to prove its divine origin ; but 
to shew, as is admitted by the antagonist in the case 
of the natural world, that the existence of difficulties 
does not furnish a logical argument against it. 

Socrates, in the Gorgias, p. 460. with the criticism of Boethius, de Syll. 
Cat. lib. ii. Opera, p. 600. 



q2 



228 APPENDIX. 



Note I. 

ON THE HYPOTHETICAL SYLLOGISM. 

That the auWoyiafjio) e^ vTroQsasctig of Aristotle are not 
identical with those which, since the time of Theophrastus 
and Eudemus, have been received in Logic as Hypothe- 
tical Syllogisms, is now generally admitted\ The word 
Hypothetical is never by Aristotle opposed to Cate- 
gorical, but to Ostensive (IsiKTmog'^) ; and he remarks that 
the Syllogistic portion of the reasoning in Hypothetical 
Syllogisms is ostensive, and requires no reduction; but 
that the determination of the original question is not 
effected by Syllogism at all, and cannot be exhibited in 
Syllogistic form. The meaning of this may be clearly 
explained by examples. 

Of the Hypothetical Syllogism, two principal kinds are 
mentioned by Aristotle. One is the aTruyooyy) sis to aduvaTov: 
the other is aSyllogismofwhich the conclusiveness depends 
entirely on agreement between two contending parties, 
and which is therefore chiefly serviceable in dialectic 
disputation. The latter may be exhibited as follows. 

The original question being to prove that some A is 

not B ; the contending parties agree to the hypothesis, 

that if some A is not C, it is not B. The reasoning 

proceeds thus : 

No X is C ; \ 

All A IS A , y (^a-vWoyto-fjios i^ v7ro6eaea>5-) 

Therefore, Some A is not C. 

And then, i7i consequence of the previous agreement, hut 
not of the Syllogism, it is allowed that some A is not B. 

^ We must except M. St. Hilaire, wlio professes to discover the ordinary 
Hypotheticals in Anal. Prior, i. 44. 1. But the text of Aristotle wiU^ardly 
Avarrant the assertion. Cf. Sir W. Hamilton's Discussions, p. 152. (2d Ed.) 

b See Anal.Pr. i. 23. 2. 



APPENDIX. 229 

The Syllogism in form is an ordinary Categorical in tlieT 
third figure ; the Conclusion, however, not being the ^ 
original question, but the antecedent of a Hypothetical ; 
Proposition, of which the question is the consequent^ 

The uTiuyoiyYi sis to d^uvurov is also Categorical, so far as 
it is Syllogistic. In this, the Conclusion syllogistically 
proved is a falsehood ; the original question being- 
inferred only by Hypothesis, because a falsehood results 
from the assumption of its contradictory''. The Hypothesis 
in this case is, that the contradictory is true®. Thus, if it 
be required to prove that some A is not B, we reason 
from the assumption of the contradictory, 
All AisBn 

All C is A; U(^^xXo7io-/x6s e| vwodea-ecos.) 
Therefore, All Cis B.j 

*= *Ev a-nacTi yap 6 [xkv avkKoyiafxhs ylverai npbs rh ix&TaKajxQav6ixivov, rh S' 
^^CLpxrjS TT^paipeTai Si^ o/moAoyias ¥i rivos &\\7]S virodecrecos. Anal. Pf. i. 23. 11. 
Th ixeTaAajix^ai/6/jL€vov is explained by Alexander as applying to the conclusion 
of the syllogism, because it is taken in a different manner from that in 
which it was originally enunciated; being at first part of a conditional 
agreement, and afterwards a categorical conclusion. For this reason, the 
syllogism is said to be /caret fieTaXri^l/iv. Anal. Pr. i. 29. 5. Were it not for 
this authority, it would seem simpler to interpret /AeraAr/il/ts merely " change 
of question ;" the disputant turning from the original question to the proof 
of another on which it is supposed to depend. Concerning the other kind 
of hypothetical syllogisms mentioned in the same passage, those KaTo. 
iroi6Tr]Ta, we have no data for even a plausible conjecture. M. St. Hilaire's 
explanation is forced. Philoponus, (Scholia, p. 178, b. 9.) says it is a 
syllogism, ck rov fxaAXov, ^ e/c rod ^rrov, ^ ck rov ujxoiov, which probably 
originated the explanation of Burgersdyck, Inst. Log. ii. 14. *' Quo scilicet 
probatur quod minus probabile est, ea couditione, ut probatum sit quod 
magis probabile est." 

^ Anal. Pr. i. 23. 8. lidvT^s yap ol Sia toD oBwdrov irepaivovTes rh fxev 
^evdos crvXKoyi^ovrai, rh S' e| ctpx^s i^ viroOeaews S^LKVVovariv '6rav a8vuar6v 
rt (rvfi^aiiyrj ttjs avri^dcrecDs TeOdarjs. I have substituted a mere symbolical 
syllogism for the instance given by Aristotle, on account of its intricacy, 
and the length requisite to expand it. The reader will find it explained 
by Waitz, vol. i. p. 430. 

"^ Anal. Pr. i. 29. 3. UaAiu d Set/crt/cws a-vWeXSyicTTai tI) A rcf E fj-rjo^ul 
virdpx^iu, vTro9efx4i/ois virdpx^tv tiv\ dia rov aSwdrov deix^VO'crai ovSevl 
vndpxou. 



230 APPENDIX. 

The Conclusion being supposed to be a known false- 
hood. 

This mode of reasoning, as exhibited by Aristotle, 
does not directly appear in the same form as the former. 
For in this the hypothesis is a premise ; the conclusion 
being the impossibility which has not been previously 
enunciated. In the former, the premises are both new 
assumptions ; the conclusion being the antecedent of 
the conditional proposition which was agreed upon as 
a hypothesis. Both, however, agree thus far, that the 
syllogistic portion of each does not differ in form from 
an ordinary Syllogism; and that in neither is the original 
question syllogistically proved. 

The notices of these Syllogisms in Aristotle are, it 
must be confessed, sufficiently scanty. Thus much, 
however, may fairly be gathered. Firstly, that, as 
regards form, they are merely the common Categorical 
Syllogisms applied to a particular purpose. Secondly, 
that their conclusiveness, as regards the original 
question, is by way of material, not of formal conse- 
quence. The syllogism by agreement obviously refers 
to dialectic disputation, and furnishes the grounds for 
a mere argumentum ad hominem, in consequence of a 
previous admission. Apart from this special appli- 
cation, which does not appear in the syllogism, the 
proof amounts to this : 

No X is C ; 
All X is A ; 
Therefore, Some A is not C. 

Therefore, (by material consequence,) Some A is not B. 

In the uTroiycoyri slg to ddvvccTov, the proof is of the same 
character. It has indeed no special reference to Dialectic, 
and is frequently employed in demonstration^; Aristotle's 

f For tlie principle of contradiction may be assumed as self-evident, 
without any convention between disputants. And in this lies the principal 



APPENDIX. 231 

own example being taken from Geometry. But still its 
connexion with the original question is not formal, but 
material ; for we assume, 

All A is B ; 

All C is A ; 
Therefore, All C is B. 

And this conclusion, from material grounds, we know to 
be false. We also know (materially again) that the minor 
premise is true ; and all that is logical in the process is 
the consequent decision that the major must be false, 
and hence, by the principle of contradiction, that the 
original question is true. 

But one step only is wanting, to convert these material 
consequences into formal ones. We have in the o-vXXo- 
y*o-jw,oj If ofjioXoyiotg clearly the germ of the Conditional 
Syllogisms of Theophrastus. It needs but to commence 
with the original hypothesis, not as a mere dialectic 
convention, but as a proposition having its own inde- 
pendent value, and we have at once a distinct form of 
argumentation, to which the Aristotelian specimen is 
related merely as a prosyllogism supporting one of the 
premises. This done, no great sagacity is required to 
see that the prosyllogism may in this, as in any other 
case, be omitted or not, according to the material 
character of the premise which it supports. 

To the dTTotycayY) slg to d^uvarov may in like manner be 
traced the origin of the Disjunctive Syllogism. The 
most natural proceeding in this case is to state the two 
contradictory propositions as alternatives, one of them 
being disproved by a prosyllogism. 

Either Some A is not B, or All A is B ; in which case 

All Cis A; 
Therefore, All C is B. 

difference between the deductio ad impossibile and the syllogism of agree- 
ment, See Anal. Pr. i. 44. 3. 



232 APPENDIX. 

This conclusion being manifestly false, we have no 
choice but to admit the other alternative. The pro- 
syllogism in this case, as in the former, may be omitted, 
if the falsehood of the alternative is evident without it. 
We have thus the Disjunctive Syllogism. 

We may agree therefore with M. St. Hilaire thus far, 
that, though the form of the Hypothetical Syllogism is not 
explicitly exhibited in the extant writings of Aristotle, 
we have nevertheless the data from which it needs but 
one step to develope it. Whether that step was taken 
by Aristotle himself in a lost work, or supplied by his 
disciples, is a point of little consequence; though 
external testimony is decidedly in favour of the latter 
supposition. 

Far more important, in a logical point of view, is the 
inquiry whether the hypothetical syllogism, by whom- 
soever analysed, is a legitimate addition to the forms 
of reasoning acknowledged in Aristotle's Organon ; and 
consequently, whether its omission can fairly be cen- 
sured as a deficiency in that work. On this question, 
I find myself compelled to hold an opinion different 
from that of the Logicians whose views have been mainly 
followed in the present work. 

By Kant and his followers, the Hypothetical Pro- 
position is described as representing a form of judgment 
essentially distinct from the Categorical; the latter being 
thoroughly assertorial, the former problematical in its 
constituent parts, assertorial only as regards the relation 
between them. Two judgments, each in itself false, 
may thus be hypothetically combined into a single 
truth ; and this combination cannot be reduced into : 
categorical form^. The Hypothetical Syllogism, in like 
manner, is a form of reasoning distinct from the cate- 

g See Kant, Logik, §. 25. Ki'ug, Loylk, §. 57. Fries, System der Logik, 
§, 02. 



APPENDIX. 233 

gorical and not reducible to it, being based on a different 
law of thought, namely, the Logical Principle of Sufficient 
Reason, a ratione ad rationatum, a negatione rationati ad 
negationem rationis valet consequential. 

Of this principle, as applied to judgments, I have 
elsewhere remarked, that it is not a law of thought, but 
only a statement of the necessity of some law or other ^ 
As applied to syllogisms, it has the same character. It 
states the fact, that whenever a condition, whether 
material cause of a fact or formal reason of a conclusion, 
exists, the conditioned fact or conclusion exists also. 
Thus viewed, it is not the law of any distinct reasoning 
process, but a statement of the conditions in which laws 
of nature or of thought are operative. When a material 
cause exists, its material effect follows, and the pheno- 
menon indicates a law of nature: when a logical premise 
is given, its logical conclusion follows, and the result 
indicates a law of thought. What law^ must in each 
case be determined by the particular features of the 
phenomenon or reasoning in question; but a statement 
of this kind is distinguished from laws of thought, 
properly so called, by the fact, that it cannot be ex- 
pressed in a symbolical form : we require the introduction 
of a definite notion. Cause, Reason, Condition, or some- 
thing of the kind, which is a special object of thought, 
not the general representative of all objects whatever. 
The principle in question is thus only a statement of 
the peculiar character of certain matters about which we 
may think, and not a law of the form of thought in general. 

It is obvious that the relation of premises and con- 
clusion in a syllogism may, like any other relation of 
condition and conditioned, be expressed in the form of 
a hypothetical proposition : " If all A is B, and all C is 

^ Kant, §. 76. Krug, §. 82. Fries, §. 58. 
" See Prolegomena Logica, p. 197. 



234 APPENDIX. 

A, then all C is B :" and the actual assertion of the 
truth of these premises will furnish at once a so-called 
hypothetical syllogism : " But all A is B, and all C is A, 
therefore all C is B." This was observed by Fries, who 
hence rightly maintains that analytical hypothetical 
judgments are formal syllogisms^. It is strange that, 
after this, he should not have gone a step further, and 
discovered that synthetical hypothetical judgments are 
assertions of material consequences. The judgment, 
"If A is B, C is D," asserts the existence of a conse- 
quence necessitated by laws other than those of thought, 
and consequently out of the province of Logic. The 
addition of a minor premise and conclusion in the so- 
called hypothetical syllogism, is merely the assertion 
that this general material consequence is verified in a 
particular case. 

The distinction so much insisted on by the Kantians, 
of the problematical character of the two members of a 
hypothetical judgment, is, like the whole Kantian doc- 
trine of modality, of no consequence in formal Logic. 
All formal thinking is, as regards the material character 
of its objects, problematical only. Formal Conception 
pronounces that certain objects of thought may possibly 
exist, leaving their actual existence to be determined by 
experience. Formal Judgment decides on the possible 
coexistence of certain concepts; and Formal Reasoning, 
on the truth of a conclusion, subject to the hypothesis of 
the truth of its premises. 

To state that this hypothesis is in a certain instance 
true, adds nothing to the logical part of the reasoning, 
but only verifies the empirical preliminaries which the 
Logician in every case assumes as given. To exhibit 
a formal consequence hypothetically, is only a needless 
reassertion of the existence of data which the act 

^ System der Loyik, §. 44. 



APPENDIX. 235 

of thought presupposes. To exhibit a material eon- 
sequence hjpothetically, is not to make it formal, but 
only to state that, in a certain given instance, a con- 
sequence not cognisable by Logic takes place. The 
sequence of " C is D," from " A is B," is not one whit 
more logical than it was before ; it is only stated to take 
place materially in the present case. 

The omission of hypothetical syllogisms has fre- 
quently been blamed as a defect in Aristotle's Organon ; 
and his French translator takes some fruitless pains 
to strain his text, in order to make out that he does 
in fact treat of them^ If there is any truth in the 
preceding observations, it will follow, that Aristotle 
understood the limits of Logic better than his critics ; 
and that his translator had better have allowed the 
omission as a merit than have attempted to deny it as 
a fault. When the hypothetical proposition states a 
formal consequence, the reasoning grounded upon it 
may always be reduced to categorical. When it states 
a material consequence, it states what the Logician, as 
such, cannot take into account. Aristotle is therefore 
quite right in saying, that in this case the conclusion : 
is not proved, but conceded"^. Syllogism may be em- 
ployed as a logical proof of the antecedent: the con- 
sequent is admitted to follow on grounds which the 
Logician, as such, does not investigate, but which may 
be warranted by the principles of this or that material 
science. 

The true character of hypothetical reasoning is lost 
sight of in the examples commonly selected by Logicians, 
which have for their subject o. proper name, and indicate, 
not a general relation of reason and consequent between 

' St. Hilaire, Loyique (TAristote Traduite en Fran<^ais, Preface, p. Ix. 
•° Anal. Prior. \. 23. 11. 



236 APPENDIX. 

two notions, but certain accidental circumstances in the 
history of an individual. The adoption of this type has 
led to the logical anomaly, that the propositions of a 
hypothetical syllogism are generally stated without any 
designate quantity; whereas it is obvious that, wherever 
concepts are compared together in any form of reasoning, 
two distinct conclusions may follow, according to the 
quantity assigned. For example, to the premise, ^' If men 
are wise, they will consult their permanent interests," 
we may supply two minors and conclusions, in the con- 
structive form, according as we affirm the antecedent of 
all men or of some. It thus becomes necessary to dis- 
tinguish between two different kinds of apparent hypo- 
thetical syllogisms, those in which the inference is from 
a general hypothesis to all or some of its special 
instances, and those in which a relation between two 
individual facts is assumed as a hypothesis leading to 
a singular conclusion. The former contain a general 
relation of determining and determined notion, which 
may always be expressed in three terms ; the occasional 
employment of four being only an accidental variety of 
language. Thus the general assertion, " If any country 
is justly governed, the people are happy," is equivalent 
to, " If any country is justly governed, it has happy 
people." This we may apply to special instances ; all 
countries, some countries^ or this country, being asserted 
to be justly governed: and this is properly hypothetical 
reasoning. The latter denote only a material connection 
between two single facts, either of which may, to certain 
minds possessed of certain additional knowledge, be an 
indication of the other ; but the true ground of the 
inference is contained in this additional knowledge, and 
not in the mere hypothetical coupling of the facts by 
a conjunction. This is not hypothetical reasoning^; 



APPENDIX. 237 

i. e. it is not reasoning from the hypothesis^ but from 
other circumstances not mentioned in the hypothesis 
at all°. 

It thus appears, that the only hypothetical judgment 
which can be employed as the real major premise of 
a syllogism, may be expressed in the form, " If any A 
is B, it is C," where A, B, and C represent concepts or 
general notions. The complete categorical equivalent 
to this is, " Every A which is B is C, because it is B," 
which admits of two interpretations, according as B 
stands for the physical cause of the fact, or for the 
logical reason of our knowing it. In the latter case, 
the judgment is analytical, and represents a disguised 
formal consequence with B as a middle term ; e. g. 
" Every man who is learned has studied, because he 
is learned." Here the notion of study is implied in 
that of learning, and the major premise is, " All learned 
beings have studied." The hypothetical proposition 
thus becomes a complete syllogism, to which the sub- 



n This may be made clearer by an example. The following is cited by 
Fries, as an instance of a hypothetical proposition, not reducible to cate- 
gorical form. " If Caius is free from business, he is writing poetry." This 
may be interpreted to mean either, generally, " whenever Caius is dis- 
engaged, he writes poetry ;" or, specially, " if he is now disengaged, he is 
now writiiig poetry." Under the former interpretation, it is a general 
hypothesis, which may be applied as a major premise to particular instances : 
but in this case the true form of the reasoning is, " All times when Caius 
is disengaged, are times when lie writes poetry; and the present is such 
a time," Under the latter intei-pretation, it is one of the cases of a 
material connection of two facts mentioned in the text. Now in this 
last case, it is obvious that the inference is really made, not from the 
hypothesis, but from some circumstance kno-\vn to the reasoner, but not 
appearing in the proposition. Any man being asked, " Why do you infer 
that Caius, being now disengaged, is writing poetry?" would reply, 
" Because he told me he should do so ;" or something of the kind. 
Assuredly he would never dream of replying, " Because if he is now 
disengaged he is writing." In this case then he does not reason from 
the hypothesis, and the expressed propositions do not compose a syl- 
logism. 



238 



APPENDIX. 



sequent consequence is related as an episyllogisni ». In 
the former case, where B stands for a physical cause, 
the judgment is synthetical, and indicates a material 
consequence, which it requires some additional know- 
ledge of facts to reduce to formal: e. g. "All wax 
exposed to the fire melts, because it is exposed." Here, 
on material grounds, we know that we cannot supply the 
premise, "All bodies exposed to the fire melt;" but 
only, "All bodies soluble by heat and exposed to the 
fire melt." In this case the consequence is extralogical, 
and requires additional data not given in the thought. 
But here also, when the judgment in question is em- 
ployed as the premise of a reasoning, the conclusion 
follows categorically ; though the premise itself cannot, 
as it stands, be proved by a prosyllogism^. 

The Disjunctive Judgment is usually described as 
representing a whole divided into two or more parts 
mutually exclusive of each other; and th« Disjunctive 
Syllogism is supposed to proceed either from the affirm- 
ation of one member to the denial of the rest, or from 
the denial of all but one to the affirmation of that one, 
by the Principle of Excluded Middle "i. 



Categorical Analysis. 
All learned beings have studied : 
All learned men are learned 



« Thus : 

Hypothetical Syllogism. 
If any man is learned, he has 

studied : 
Some men are learned ; 
'. Some men have studied. .'.All learned men have studied : 

Some men are learned men ; 
. Some men have studied. 
P The analysis in this case may be exhibited thus : 



Hypothetical Syllogism. 
If any wax is exposed to the fire 

it melts : 
This wax is exposed to the fire ; 
.• . This wax melts. 
The parenthesis indicates the material ground of the major premise, 
q Kant, §. 27 sqq. 77, 78. Krug, §. 57, 84, 85. Fries, §. 33, 59. 



Categorical Equivalent. 
AU wax exposed to the fire melts 

(because exposed) : 
This wax is exposed to the fire ; 
.*. This wax melts. ^~ 



APPENDIX. 239 

This can scarcely be regarded as a correct analj^sis of 
the process, unless the two members are formally stated 
as contradictory. The Principle of Excluded Middle 
asserts that every thing is either A or not A, that of two 
contradictories, one must exist in every object; as the 
Principle of Contradiction asserts that they cannot both 
exist. But if the two members are not stated as contra- 
dictories, if my disjunctive premise is, "All C is either A 
or B," I make the material assertion that All C which is 
not A is B. If then I reason, " This C is not A'^, there- 
fore it is B," I employ the Principle of Identity in addi- 
tion to that of Excluded Middle. Again, if I maintain 
that No C can be both A and B, I make the material 
assertion that No C which is A is B ; and from hence to 
reason, "This C is A, therefore it is not B," requires not 
the Principle of Excluded Middle, but that of Contra- 
diction. In the first case, the Excluded Middle does 
not lead directly to the conclusion, but only to the con- 
traposition of the minor premise. When we deny this 
C to be A, this principle enables us to assert that it is 
not-A, and hence to bring the reasoning under the Prin- 
ciple of Identity. But in the second case, in which one 
of the opposed members is affirmed^ the ground on which 
we deny the other, is not because both cannot be false, 
but because both cannot be true. 

It may be questioned whether this second inference is 
warranted by the form of the disjunctive premise. Boe- 
thius calls it a material consequence^ ; and, in spite of the 
many eminent authorities on the other side, I am still 
disposed to think he is right. But let us grant for a 
moment the opposite view, and allow that the proposition, 
" All C is either A or B," implies, as a condition of its 

•■ The indefinite minor, "but it is not A," is as objectionable in this 
syllogism as in the conditional. 

* Be Syll. Hyp. lib. i. Opera, p. 616. Cf. Galen. Isagoge Dial. p. 11. 



240 APPENDIX. 

truth, " No C can be both*." Thus viewed, it is in reality 
a complex proposition, containing two distinct asser- 
tions, each of which may be the ground of two distinct 
processes of reasoning, governed by two opposite laws. 
Surely it is essential to all clear thinking, that the two 
should be separated from each other, and not confounded 
under one form by assuming the Law of Excluded 
Middle to be, what it is not, a complex of those of 
Identity and Contradiction. Thus distinguished, the 
moods of the disjunctive syllogism are mere verbal 
variations from the categorical form, and may easily be 
brought under its laws ^ 



* Aquinas, Opusc. xlviii. De Enunciatlone, c. xiv. Ki'ug, Logik 
1 Thus: 

Modus tollendo ponens. 
Every C which is not A is B. 
Every ^ 

Some |-C is a C which is not A. 
This i 
•.ItisB. 



Modus ponendo tollens. 
No C which is A is B. 
Every \ 

Some r C is a C which is A. 
This ) 
.'. It is not B. 



The first is governed hy the Principle of Identity, and the second by the 
Principle of Contradiction. 



APPENDIX. 241 



Note K. 
on the demonstrative syllogism. 

Scientific knowledge {ro sTrhrad^oLi)^ except when of 
axiomatic principles ''', requires a conviction of the neces- 
sity of the proposition known, and a knowledge of its 
cause''. This is produced by the Demonstrative or 
Scientific Syllogism, which, according to Aristotle's 
definition, is e^ uKri^cLv koc) TrgcuTcov xu) df^ecroov koc) yvcogi[jt,a}' 
Tegctiv KOi) TrgoTsgcjQV xal ahtcov rov av^'KegaoriioLTO^^. As the 
conclusions of this Syllogism are necessary, so must 
also be the premises ; this necessity consists in their 
being 'per se, in either the first or the second sense of 
that expression*^. If any of these conditions are not 
complied with ; e. g. if the premise, though containing 

a In the strict sense of the terras, iiria-raadai is said of necessary truths 
which we receive by deduction from higher truths ; vo€7v, of those which we 
receive as evident of themselves. Hence the principal meaning of the 
corresponding terms, iirKTriiixT] and vovs. The latter, however, or rather its 
result, is sometimes called eTrto-r^/xTj avairSSeiKros. Cf. Anal. Post. i. 3. 2, 3. 
i. 33. 1. ii. 19. 7. Eth. Nic. vi. 9. 9. The word '6poi, in the first and last of 
these places, does not mean, as Pacius explains, simple terms, hut, as 
M. St. Hilaire renders, '• les propositions immediates," i. e. axioms — the 
limits from which Demonstration commences. 

b Anal. Post. i. 3. 1 . 

<^ Anal. Post. i. 2. 2. By Jirst and immediate are here meant the same 
thing ; i. e. not demonstrable by a middle term from any higher truth ; 
yvcapifMcaTepa sc. (pvcrei, not rjfuv, i. e. more universal. 

^ Of necessity, three degrees are enumerated. Anal. Post. i. 4. Kar^ 
iravrSs, /ca0' avrd, and ^ avrS; usually rendered, de omni, per se, and 
quatenus ipsum. Of per se, as applied to a proposition, four senses are 
given. 1. When the predicate is part of the definition of the subject. 
2. When the subject is part of the definition of the predicate. 3. When 
existence is predicated of a substance. 4. When the subject is the external 
efl&cient cause of the predicate. Propositions in Demonstration proper 
must be per se either in the first or second meaning. See Anal. Post. i. 



R 



242 APPENDIX. 

the cause of the conclusion, is not the first cause, (in 
which case the syllogism is not 1^ ajxeVwvej or if the 
premise be an effect and not a cause of the conclusion, 
or if the premise, though immediate, be a remote and 
not a proximate cause of the conclusion, — under these 
circumstances, there is no Demonstration, in the proper 
sense of the term, as we only know the fact, but not the 
caused 

From the above data, the scholastic successors of 
Aristotle have constructed the following specimen of 
demonstratio jootissima, 

Omne animal rationale est risihile ; 
Omnia homo est animal rationale : ergo 
Omnis homo est risibilis. 

In this syllogism all three propositions are per se ; 
the major premise and the conclusion in the second 
manner; for the subject ^owo, and consequently awm«/ 
rationale, forms part of the definition of the attribute 
risihile : the minor premise is per se in the first manner ; 
for animal rationale, its predicate, is the definition of 
homo. 

In all the propositions of this Demonstration, the 
predicate and subject are coextensive, and the pro- 

e From this it may fairly be inferred that the demonstratio propter quid 
sit per causam non primam, would not alone be regarded by Aristotle as a 
Demonstration, though it may form a subordinate portion of a complex 
Demonstration. The ambiguity of the word ^/ietros, which has partly led 
to the discrepancies on this point, has been explained before. See p. 119. 

f See Anal. Post, i, 13. The distinction between demonstratio propter 
quid potissima and non potissima cannot fairly be attributed to Aristotle. 
The whole of the chapters of the first book of the Posterior Analytics, from 
the first to the thirteenth inclusive, treat of one kind of Demonstration 
only. The passages in the second book, (ch. 17 and 18.) which seem to 
favoui' the distinction, are treating only of the inferior sense of Demon- 
stration, in which it is applicable to to irecpvKOTa ws iirl rh iroXv. Cf. Anal. 
Pr. i. 13. 5, 6. An. Post. i. 8. 3. i. 30. 



APPENDIX. 243 

position simply convertible. This is requisite, in order 
to comply with the condition of quatenus ipsum. 

This Demonstration is exceedingly satisfactory, if we 
are only allowed to assume all the conditions on which 
its validity depends; viz. 1. that risibility does flow as 
an effect from rationality as a cause; 2. that the major 
premise, in which this causation is asserted, is an 
axiomatic principle, cognoscible a priori, and, as such, 
carrjdng with its cognition, the conviction of necessity ; 
3. that the conclusion is not a mere repetition, in dif- 
ferent words, of the major premise ; homo and animal 
rationale being identical ; 4. that any Demonstration 
acknowledged to be valid can be resolved into the above 
form. 

But w^aiving the consideration of these questions, 
which are more easily asked than answered^, we may 
find a simpler way of testing the demonstratio potissima, 
by going back to the original authority. For Aristotle's 
examples are principally taken, as is natural, from the 
Mathematics; and it is to a Geometrical theorem that the 
tests of xa6' auTo and ^ olvto are expressly applied"*. Can 
it be believed, then, that Aristotle regarded the following 
as a correct analysis of Geometrical Demonstration } 

Every rectilinear figure of three sides has its angles equal 

to two right angles ; 
Every triangle is a rectilinear figure of three sides ; therefore 
Every triangle has its angles equal to two right angles. 

& " Si scrupulosius inquiratur in rem banc ; Num qua sit essentialis 
connexio inter ration alitatem et risibilitatem, quo sit ea propria causa hujus, 
seu causa per se ; ut Kationalitas, propter ipsam sui Essentiam, non possit 
esse absque Eisibilitate ; neque hsec absque ilia : et quidem immediata, 
absque interventu alius considerationis qua connectatur ; atque adcBquata, 
ut ad omnes rationales extendatur atque ad bos solos : subtilior forsan 
esset inquisitio quam ut ei facile satisfiat." Wallis, Log. lib. 3. cap. 22. 

^ Anal. Post. i. 4. 6. Kat t^ rpiydoucf ^ rplywvov 8vo opQai Koi yap Ka6' 
avrh rh rplyuvou 5vo opQais tcrov. 

R 2 



244 APPENDIX. 

It is not denied that there are passages in Aristotle 
which may seem to countenance this interpretation ; but 
there are others so palpably inconsistent with it that 
we are compelled to seek for a new explanation of the 
former. 

In the first place, Aristotle distinctly condemns the 
assumption of Definitions as a Petitio Princijni^ a charge 
to which the above example is obviously liable ; the real 
question to be proved being, that the three-sided figure 
has its angles equal to two right angles, whether it is 
called a triangle or not. In the second place, he says 
that Demonstration proceeds from axioms, and cites 
as a specimen of the latter, " If equals be taken from 
equals, the remainders are equal ''." These axioms, 
he says, are common to many classes of objects ; but, 
in any single Science, need only be assumed to an 
extent commensurate with the object-matter of that 
Science. The above axiom, for example, is true of 
other things besides Geometrical Magnitudes, but it is 
suflicient for the Geometer to assume it as true of these 
only. 

Now if an axiom of this kind be the major premise in 
a Demonstration, it is manifest that its predicate will 
also be the predicate of the Conclusion ; and that the 
logical form of that Conclusion will be, not "All 
triangles are figures having their angles equal to two 
right angles," but, " Triangles and figures having their 
angles equal to two right angles are equal to each 
other." 

The immediate Syllogism from which this proposition 
is proved by Euclid, may be logically stated as follows : 



» Top. viii. 13. 2. 

k Anal. Post. i. 7. l.i. 10.2. 



APPENDIX. 245 

" Magnitudes equal to the adjacent exterior and interior 
angles of a triangle are equal to each other ; 

The three interior angles and two right angles are equal to 
the adjacent exterior and interior angles ; 

Therefore, they are equal to each other." 

The major premise of this Syllogism is an immediate 
deduction from the first axiom ; thus : 

"Magnitudes which are equal to the same are equal to 

each other ; 
Magnitudes equal to the adjacent exterior and interior 

angles are equal to the same ; 
Therefore, they are equal to each other i." 

That the true syllogistic analysis of Geometrical Demon- 
strations will always be in this form, the axioms standing 
as major premises, and the constructions in each case 
furnishing the proper minor, is evident. It only remains 
to see whether the text of Aristotle can be accommodated 
to this interpretation as well as to the other. 

With some passages it evidently tallies much better. 
The places in which the axioms are mentioned in 
connexion w4th demonstration have never been satis- 
factorily explained on the scholastic interpretation"". 
There are others which prima facie appear to favour 



1 See Wolf, Philosophia Bationalis, §. 492. 551. 552. 798. Mill, Logic, 
vol. i. p. 285. Sir W. Hamilton, Eeid's Works, p. 702. 

"> The diflficulty is evaded rather than surmounted by distinguishing 
immediate propositions from axioms, and saying that the latter are employed 
in demonstration virtually but not actually. Aquinas, Opusc. 48. de Syll. 
Dem. cap. 6. Cf. Zabarella, in I. An. Post. Cont. 57, 58. Crakanthorpe, 
Log. lib. iv. cap. 1. For, in the first place, Aristotle expressly calls the 
axioms immediate principles of syllogism, and principles from which we 
demonstrate. In the second place, any principle which virtually enters and 
confirms the premises of a demonstration must, if the syllogistic theory be 
worth any thing, be capable of syllogistic connexion with the premises which '> 

it confirms : and until this connexion is formally exhibited, no demon- ' 

stration can be logically complete. 



246 APPENDIX. 

the latter ; but, when both interpretations require some 
straining- of Aristotle's language, it is due to the memory 
of the Father of Logic to give him the benefit of that 
which does not convict him of flagrant error in the 
application of his own principles. 

Referring back to the Syllogism above given, the major 
premise may fairly be regarded as per se ; the subject 
forming part of the definition of the predicate. For 
Equality, in the limited sense in which it is employed 
in Geometry, is a property of Magnitudes; and the 
latter, as the first and proper subject, will appear in 
the definition of Geometrical Equality. This definition 
has been found by some Geometers in the eighth axiom 
of Euclid; "Magnitudes which coincide are equal;" 
which, stated in the Aristotelian form, would be, 
" Equality is the Coincidence of Magnitudes^" 

The mingr premise may also be considered 0^% per se. 
For our definition of a right angle is, that it is half the 
sum of the two adjacent angles formed by one straight 
line with another ; and our notion of two right angles is 
that of the sum of the same two adjacent angles. As 
regards the Conclusion, we need not trouble ourselves 
with reducing it to the requisite conditions, inasmuch as 
it is expressly said by Aristotle to comply with them. 
This compliance does not directly appear in the only 
form in which the proposition can be syllogistically 
proved ; but in the equipollent statement, that the 
triangle is a figure of which the interior angles are equal 
to two right angles. The predicate in this case states a 
property of the triangle, in the definition of which 
property, if any be attempted, the proper subject must 
be included. 

A demonstration of this kind certainly falls short, in 
some respects, of the scholastic model. The predicate 
" Cf. Stewart, Elements, Part II. ch. iii. Sect. ii. 2. 



APPENDIX. 247 

and subject in each proposition, as stated, are not con- 
vertible ; and the middle term is not a definition of the 
minor. But of these requisitions, the first seems to be 
founded on an erroneous interpretation of Aristotle, 
according to which that Philosopher is supposed to 
speak of the Propositions as they appear when strictly 
enunciated in logical form; not (as seems more probable) 
of the same Propositions as ordinarily stated by the 
Geometer*'. With regard to the second condition, the 
text of Aristotle does not warrant its imposition. He 
says indeed, that the middle term in demonstration must 
be a definition of the major^; and the precept is intel- 
ligible enough, if we rightly understand his theory of the 
Definition of Attributes. As regards the minor term, it 
would be difficult to produce a single passage where this 
condition is clearly laid down as a law of Demonstration; 
and there is more than one with which it w^ould be no 
easy task to reconcile it. 

If it be thought somewhat over-bold to repudiate 
positions which so many eminent Logicians have 
regarded as legitimate deductions from the text of 
Aristotle ; it must be remembered that w^e have other 
data for interpretation besides the mere weight of autho- 
rity. Aristotle's theory of demonstration is principally 
framed wdth reference to Geometry : the Scholastic 
examples, on the other hand, are Physical. The medi- 
aeval state of Physical science was perhaps such as to 
justify, or at least to account for, the Logical and Meta- 
physical fictions connected with it, and to give a seeming 
validity to the most potent demonstration of Risibility as 
an emanation from Rationality; though that emanation 

o In this way we may interpret such passages as Anal. Post. i. 4. 6. i. 5. 
6.ii. 17.3. 

P Anal. Post. ii. 17. 3. The meaning of this has already been explained. 
See note C. 



248 APPENDIX. 

was never dreamed of by Aristotle, and will scarcely claim 
implicit belief in the present day. But it is not merely 
because the revolution effected in this branch of Science 
has invalidated the individual example, that the inter- 
pretation is objected to ; but because the words of Aris- 
totle himself expressly direct us to another criterion. 
The Demonstrations of Geometry are still extant in the 
same form in which they existed in the days of the 
Stagirite. Though Euclid himself, the oldest remaining 
Geometer, is a few years younger than Aristotle •*, yet, 
except on the very improbable hypothesis that he was 
the original inventor of the whole contents of his 
Elements, that work must be regarded as furnishing a 
fair specimen of the demonstrations treated of in the 
Posterior Analytics. By this touchstone, Aristotle and 
his interpreters may be tested. When any modern 
Herlinus or Dasypodius' shall exhibit a single demon- 
stration of Euclid in the form of a scholastic demonstratio 
potissima^ we may then recognise this foundling of the 
Schoolmen as the legitimate offspring of their master^ 
Till that is done, we must continue to believe that 
Aristotle was sufficiently acquainted with the use of his 
own instrument, to be able to give a correct Logical 
Analysis of the Demonstrations of Geometry. 

q Euclid floiurislied in the reign of Ptolemy Lagus, B.C. 823—283. This 
period, however, probably corresponds to the close, not to the commence- 
ment, of his life. This would make him partly contemporary mth, though 
about thirty years junior to, Aristotle. 

r Of the remarkable work of these two "zealous but thick-headed 
Logicians," as Sir W. Hamilton calls them, a specimen will be found in 
the next note. 

8 See on this point the criticisms of Ramus, Scholce Mathematicce, 1. ui. 
and of Wolf, Phil. Bat. §. 498. Both, however, treat the scholastic form as 
Aristotehan. 



APPENDIX. 249 



Note L. 
on the logic of geometry. 



The Propositions which have been regarded by- 
different writers as constituting the foundation of geo- 
metrical demonstration, may be classified as follows. 

I. Definitions, analysing the complex notions of the [ 
several magnitudes or figures. 

II. Postulates, assuming the existence of the objects ' 
defined. ' 

III. Axioms proper to Geometry, or synthetical judg- f 
ments, stating self-evident properties of certain magni- ^ 
tudes. 

. IV. General axioms % or analytical judgments, logically j 
/involving the notions of equality or inequality. 

Some one or more of these, under various names, (for 
the language of the several writers has been by no 
means uniform,) have been selected at different times 
as the fundamental assumptions or premises fi'om which 
the conclusions of Geometry may be demonstrated. A 
brief examination of each may perhaps help to clear the 
question. 

I. According to Stewart, the properties of geometrical 
figures follow from the Definitions of those figures ; the 
general axioms being mere barren truisms, and the 
axioms proper, (such as the 10th, 1 1th, and 12th of Euclid,) 
being theorems requiring demonstration. In this theory, 

* I have retained the language of the modern editions of Euclid, as 
that most familiar to the majority of readers. At the same time it may 
be observed, that this language departs widely from the original text of 
Euclid himself. In that text the general axioms are called common 
notions (/cotvai iuvoiai), while the axioms proper are included among the 
postulates (atTrj^aTo). 



•250 APPENDIX. 

mathematical necessity becomes identified with logical, 
being only the result of the harmony of a process of 
thought with its original assumption. This consequence 
is accepted by Stewart himself, as well as by Archbishop 
Whately, who speaks of the denial of geometrical pro- 
positions as self-contradictory^ . 

This view may be refuted either directly or by a 
reductio ad ahsurdum ; for, firstly, it rests on an un- 
tenable assertion ; secondly, it leads to an inadmissible 
consequence. 

Firstly. If the properties of a figure follow from the 
definition of that figure, it must either be because they 
are implied in some one attribute of that definition, or 
because they are implied in the whole. A triangle e. g. 
will have its angles equal to two right angles, either 
because it is a rectilinear figure, or because it is of three 
sides, or because it is both. The two first suppositions 
are manifestly false : the third begs the question ; for 
why the notion of a triangle, regarded as a complex 
whole, has this property, is the very point at issue. 

Hence it appears that the Definitions of Geometry, so 
far as they are employed in demonstration, are merely 
nominal. From the analysis of the complex notion no 
conclusion is derived. The Definition only serves to 
connect the notion as a whole wath the name triangle. 
The question, w^hy a rectilinear figure of three sides, be 
it called triangle or not, has its angles equal to two 
right angles, remains unanswered. 

Secondly. If geometrical reasoning is merely "the 
logical filiation of consequences which follow from an 
assumed hypothesis," there is no reason why its con- 
clusions should be more important than those of any 

b This view is also adopted by M. Cousin in Ms Lectures on Kant, 
apparently as an exposition of the opinion of Kant himself, to \^ch 
however it is diametrically opposed. 



APPENDIX. 251 

other analysis of imaginary notions, such as (to use ? 
Mr. Mill's illustration) a deduction of the physiological 
properties of an imaginary animal, or the political 
history of an imaginary commonwealth. The whole 
character and history of mathematical science militates ^ 
against the admission of this consequence. 

II. Mr. Mill, while agreeing with Stewart that mathe- 
matical necessity is merely hypothetical and conse- 
quential, saw clearly that Stewart's doctrine concerning 
Definitions was untenable. This led him to adopt the 
second theory, according to which geometrical inferences ' 
depend on Postulates assuming the existence of the 
objects defined. Thus a triangle has its angles equal 
to two right angles, because there may really exist a 
rectilinear figure having three sides ; and this existence 
is implied, though not verbally expressed, in the defi- 
nition. 

This theory derives some apparent support from the 
use of the principle of superposition. When, for instance, 
the demonstration of the fourth proposition of Euclid 
supposes the triangle A B C to be applied to the triangle 
D E F, it clearly assumes the existence of both triangles, 
not merely as general notions, which are identical in 
thought, but as distinct individual magnitudes, occupy- 
ing space, and capable of being transferred from one 
position in space to another. One non-entity cannot be 
applied to another. Thus far Mr. Mill's position is 
unquestionably true ; but 1 think it may be shewn to be 
not itself the fundamental assumption of Geometry, but 
a consequence derivable from a higher assumption. 

The existence is clearly only that which is implied in 
the possible construction of the figure. The actual or 
possible existence in nature of a body so figured is not 
once appealed to in the demonstration, and might be 
denied without affecting its validity. The Postulate, 



252 APPENDIX. 

therefore, implies the possible construction of a figure, 
such as is contemplated in the proposition. 

But this construction is mental, not manual. The 
figure as drawn upon paper is only a representative of 
the figure as imagined by the mind, and might be dis- 
pensed with altogether if the latter could be kept before 
us with sufficient steadiness. This brings us to Kant's 
principle of the possibility of mathematical science, viz. 
the power of constructing the objects of its concepts ; 
i. e. of presenting them a priori in a pure intuition. 

But how is this construction itself possible, and what 
conditions is it required to fulfil } Mr. Mill regards it 
as only possible a posteriori, and as subject to the same 
conditions as an object of sense. He says, " the points, 
lines, circles, and squares, which any one has in his 
mind, are simply copies of the points, lines, circles, and 
squares which he has known in his experience. We 
can reason about a line as if it had no breadth ; but we 
cannot conceive a line without breadths" This is true ; 
but the author is mistaken in supposing such a con- 
ception to be necessary to establish the a priori character 
of Mathematics. The true Postulate is not that of the 
possible existence of an object corresponding to the 
definition, but of one fulfilling the conditions of the 
proper axiom. We are not required to conceive a 
straight line as length without breadth : we are required 
to conceive it as such that two straight lines cannot 
enclose a space. The definition itself is but an im- 
perfect attempt to describe in general terms w^hat is 
known much more clearly by the image. It may serve 
to lead the thoughts of the learner to the proper image ; 
but it was itself founded on a previous image in the 
mind of the teacher; and if the definition and the image 
differ, the former is in fault, not the latter. -~ 

e Logic, b. ii. ch. v. 



APPENDIX. 253 

III. This brings us to our third theory, which is that 
maintained bj Kant. According to this theory, the 
fundamental assumptions of Geometry oxe Prober Axioms, 
or synthetical judgments a priori; and the possibility of 
forming such judgments depends on the power of con- 
structing the objects to which they refer in a pure 
intuition, i. e. in an intuition containing no adventitious 
element external to the mind itself. The images of 
geometrical figures differ from all others in being, not 
represented modifications of body, but presented modi- 
fications of space ; and the universal validity of the 
synthetical judgments is a consequence of the universal 
presence of space as the form of every possible per- 
ception of body. 

Three of these synthetical judgments are given in the 
10th, 11th, and 12th axioms of Euclid; and either these 
or other axioms analogous to these must be assumed as 
evident by intuition, before any of the properties of 
more complex figures can be made known by demon- 
stration. I do not say that Euclid has given the best 
and simplest forms of these axioms, but that in some 
form or other they are indispensable. To regard all 
such axioms as possibly demonstrable theorems is to be 
ignorant of the logical conditions under which demon- 
stration is possible; for a synthetical judgment is de- 
monstrable only on the condition that another synthetical 
judgment may be assumed. 0» yoiq uTravToov tl,YiTovvTss \oyov 
ccvaigov(ri Xoyov. 

It may be true that the image which gives rise to the 
intuitive perception of the axiom, is not consciously 
contemplated as more perfect than the corresponding 
figure as seen in a body; but this does not prove that 
the axiom is really generalized from the latter. The 
inadequacy of sensible magnitudes for mathematical 
certainty does not arise from that of which we are 



254 APPENDIX. 

immediately conscious, but from that of which we are 
not. The straight line as perceived is a quality of body; 
the straight line as imagined is a modification of space. 
The portions of the two actually presented at any time 
may not apparently diifer from each other; but our 
empirical knowledge or ignorance of body may suggest 
actual or possible variations not perceived in the in- 
tuition; for the qualities of body have an objective 
existence independently of our perception, and therefore 
may or may not be adequately perceived at any one 
time. We see, for example, that a line running along 
the earth's surface is apparently straight; but we know 
that it is in reality an arc of the earth's curvature, and 
might be seen to be so in another position or with more 
acute organs. But the straight line in space exists only 
as imagined, and is imagined only as mathematically 
exact. The intuition, therefore, is adequate and valid 
for any extent of space, and in any portion. The 
apparent straightness of the visible line is the result of 
an imperfection in our bodily organs ; and with more 
acute senses we might perceive its deviation. The 
presented straightness of the imaginary line results from 
the exactness of our constructive power ; and a superior 
excellence in this would only enable us to extend the 
same image to a greater length, or to retain it more 
steadily before the mind. 

IV. The Synthetical Axioms are thus the ground of all 
that is properly geometrical in our fundamental assump- 
tions ; but the Analytical Axioms are employed also, as 
expressing general conceptions of equality and inequality 
under which geometrical magnitudes may be brought. 
Stewart was led into his erroneous view of definitions by 
his contempt for the syllogism, which he would not 
allow to be under any circumstances the type of demon- 
strative reasoning. In this contempt Mr. Mill does not 



APPENDIX. 255 

participate, and he has accordingly exhibited the fifth 
proposition of Euclid demonstrated in syllogistic form. 
In this demonstration we see both analytical and syn- 
thetical axioms employed as major premises ; the former 
as general formulae, founded on the conception of 
equality; the latter as the means of applying this 
general conception to geometrical magnitudes, in which 
the test of equality is coincide7ice. One or the other will 
be employed in different syllogisms, according as the 
major term to be proved is equality or coincidence. The 
minor premises are furnished by the conditions, given or 
constructed, of the particular figure. 

Against the form of the geometrical syllogism as 
exhibited by Mr. Mill the logician will have no ob- 
jections to allege ; though the metaphysician will not be 
disposed to acquiesce in his statement that the axioms 
of both kinds are gained by induction. And it is not 
strictly accurate to represent the first three axioms of 
Euclid as capable of proof by an imaginary super- 
position. To the axioms in their general form this prin- 
ciple is inapplicable ; for coincidence is not the test of 
equality in general, but only of equality in superficial 
magnitudes. To the axioms as employed in Geometry 
the principle of superposition may be applied : but even 
here it adds nothing to their evidence. Magnitudes 
given as the sums of equal magnitudes are ipso facto 
thought as equal ; and to have recourse to super- 
position tends to confound the evidence of logical 
necessity resting on the laws of thought with that of 
geometrical necessity resting on the conditions of in- 
tuition. 

Much error and confusion on this subject might 
have been avoided, had modern philosophers observed 
Aristotle's distinction between a^%at 10 coy, or assumptions 
from which we reason, and «g%ai Treqi o, or assumptions 



25G APPENDIX. 

about the objects of our reasoning. In the former class 
he rightly places the axioms; in the latter, the definitions. 
But the true distinction between the axioms proper 
and the definitions, as synthetical and analytical judg- 
ments, has not, I think, been as yet accurately carried 
out in reference to Geometry. 



The above remarks were written as an appendix to 
a pamphlet of mine on the Limits of Demonstrative 
Science, published in 1853. In the remainder of this 
note, I propose to resume a question which was then 
only partially considered, and to point out what appears 
to be the chief deficiency in the logical arrangement of 
geometrical principles. 

Plato asserted that mathematical demonstration was 
founded on hypotheses^. Aristotle in like manner enu- 
merates hypotheses, along with definitions, among the 
proper principles of science ^ By this term both philo- 
sophers appear to have meant the same thing ; namely, 
that the real existence of the objects of demonstration is 
not proved, but supposed. If there exist any where 
two perfect straight lines, those lines cannot enclose 
a space ; and if there exists any where a figure formed by 
three such lines, it has its angles equal to two right 
angles. But this supposed existence of the objects 
cannot be verified by any process of mathematical 
reasoning. To bridge over the chasm which separates 
thoughts from things ; to determine how far a subjective 
necessity of thinking indicates a corresponding objective 
necessity of existence, is the office, not of Mathematics, 
but of a Science of Being, of Metaphysics, or, as Plato 
would say, of Dialectic. 

But though objective existence is beyond the province 

d Rep. vi. p. 510. C. « Anal. Post. i. 2. 7, 



APPENDIX. 257 

of the mathematician, there is a further condition of 
subjective existence, which he is bound to verify for 
himself, by an appeal to pure intuition; i. e. by con- 
structing in his mind an image corresponding to each 
assumed conception. As far as mere nomenclature is 
concerned, we might employ the term Mangle to denote 
a rectilinear figure of two sides, or the term hieentrical 
circle to denote a figure in which all straight lines drawn 
from two interior points to the circumference are equal 
to each other. There is no logical contradiction in 
such definitions; and those who maintain that all 
mathematical certainty depends on experience, are 
bound in consistency to admit that these conceptions 
are no more absurd than those of a centaur or a hippo- 
gryph; representing objects no otherwise inconceivable 
than that experience has shewn them to have no real 
existence. 

Hence it follows, that no expression in Geometry 
which combines together a plurality of attributes can be 
regarded as a pure definition. For the assumption that 
such attributes can coexist in an image or figure is either 
demonstrable or indemonstrable. In the former case 
the definition is coupled with a theorem, in the latter 
with an axiom. Thus, for example, to define a triangle 
as a rectilinear figure of three sides involves the as- 
sumption, that three straight lines can enclose a space, 
which is quite as much an axiom as the assumption 
that two cannot. Again, to define an acute angled 
triangle as one that has three acute angles involves the 
assumption, that three straight lines inclined at acute 
angles to each other will enclose a space. Accordingly 
we find in the ordinary editions of Euclid many of the 
definitions accompanied by figures, which furnish an 
evidence of the possibility of the conception by a direct 
appeal to the intuition. 



258 APPENDIX. 

From this we may conclude that the numerous attempts 
of Geometers to diminish or get rid of their axioms have 
been steps in a wrong direction. The number of 
axioms, instead of being diminished, should be very 
considerably increased; and the errors that have hitherto 
prevailed on the nature and foundation of Geometrical 
reasoning have been mainly owing to the manner in 
which many indispensable assumptions have been either 
omitted altogether, or concealed among the definitions. 

Some valuable hints on this point may be gathered 
from a very able and interesting paper by Professor De 
Morgan, printed in the Companion to the Almanac for 
1849. The following extracts indicate a principle which 
might be pursued to further results. 

" Book I. Definitions. Of these, iii, vi, xiii, are obvious 
statements, but not definitions of words ; viii, xxvi, xxxi 
to xxxiv, are never subsequently used; xviii, if semicircle 
have its etymological meaning, as seems the intention, 
is a theorem, which ought to be iii. 1. The remaining 
definitions are of two kinds: first, those which do not 
explain their terms, but demand a notion already existing 
in the student's mind; they are i, ii, iv, v, vii, ix: secondly, 
purely verbal definitions ; they are x, xi, xii, xiv to xvii, 
xix to XXX, and xxxv. Insist on angle as a magnitude ; 
on the comparison of angles as to greater, equal, or less, 
by superposition ; on the rights of angles equal to and 
greater than two right angles. The angle made by a 
straight line with its own continuation is a definite 
angular magnitude ; and its half is the best definition 
of a right angle. It is to be regretted that there is no 
single phrase for " two right angles." 

" Postulates and axioms : In Euclid, postulates and 
common notions. All Geometrical demands are postulates 
in Euclid; his axioms or common notions are in every 
instance notions common to all kinds of magnitude as 



APPENDIX. 259 

well as space magnitudes. Restore this; that is, let 
the postulates be, Simson's postulates, and axioms, x, xi, 
xii ; but instead of xi, substitute " if two right lines 
coincide in two points, they coincide when produced," 
as more self-evident. From this it is seen that the 
doubles of all right angles are equal, and thence that 
all right angles are equal ; and this should come between 
I. 12. and I. 13. as a proof of the theorem, "all right 
angles are equal." For xii substitute " two lines which 
cut one another are not both parallel to any third line," 
from which, after I. 28. prove Simson's axiom xii as a 
theorem. Remark that the distinction of postulate 
and axiom, as 'problem and theorem^ could not have been 
Euclid's notion, for he does not recognise the last 
distinction ; both are with him simply propositions. 
The expressed six postulates of Euclid are not the 
only ones which occur ; others are tacitly adopted, as 
will presently appear. Nothing should be tacitly assumed 
by those who will not assume without express statement, 
that " two straight lines cannot inclose a space." 

"I. 1. The following postulates are demanded: "if 
two figures which have one or more points in common 
have each a point which is not in the other, the bound- 
aries of those figures must cut," and " every point is 
without or within a circle, according as its distance 
from the centre is more or less than the radius." With 
less, the intersection of the circles cannot be proved. 
I. 4. This postulate is assumed, " any figure may be 
removed from place to place without alteration of form, 
and a plane figure may be turned round on the plane." 
But for this right to turn, I. 4. would not prove I. 6." 

In the general principles of Professor De Morgan's 
criticism I fully concur, though slightly differing from 
one or two of his details. Definitions iii. and vi. are syn- 
thetical judgments, not developing the conceptions of 

s 2 



200 APPENDIX. 

the point and straight line, but affirming a property of 
each. These then should be classed among the axioms, 
or", as Mr. De Morgan more properly terms them, the 
postulates. Definitions i, ii, iv, v, vii, viii, ix, are not 
really employed as conceptions, but only serve to refer us 
to the corresponding intuition ; which in every case is 
the basis of one or more axioms, implied, if not expressly 
stated. Among such axioms must be classed the follow- 
ing assumptions. '' Two lines can meet each other, and 
the place where they meet is always a single point." 
" Two lines can intersect each other, and the place 
where they intersect is always a single point." 
(These are properties of the point, and assumptions of 
the possibility of angles.) "A straight line may lie in 
and form part of a superficies." Definitions xiii, xiv, 
xvi, are the only purely verbal ones ; for Definitions x, 
xi, xii, and xvii, assume that straight lines can be drawn 
to comply with certain specified conditions; and the 
others, being definitions of figures, assume that lines 
under specified conditions can enclose a space. 

The above remarks will sufficiently shew in what 
respects the attempts of Geometers to dispense with 
axioms have failed. They have not been aware that 
every synthetical judgment assumed without demon- 
stration is a axiom. They have attempted to deal, not 
very successfully, with the expressed axioms of Euclid; 
but they have neglected, and in their own attempts have 
assumed, principles equally axiomatic, though only 
understood; and they have not been aware that an 
assumption resting on an appeal to the senses or to 
the imagination is as much an unproved assumption as 
one which appeals to the thought; for of the one we 
can only say that we are so constituted that we cannot 
but perceive it, and of the other, that we are so con- 
stituted that we cannot but think it. 



APPENDIX. 261 

An ingenious and instructive but unsuccessful attempt 
of this kind is made in Colonel Thompson's " Geometry 
without Axioms." The author every where identifies 
intelligible magnitudes with sensible; and this identifi- 
cation gives rise to a multitude of subordinate assump- 
tions, inadmissible in strict demonstration, but which, if 
admissible, would be as much axioms as any thing in 
Euclid. By identifying intelligible magnitudes with 
sensible, it is implied that all the perfections which are 
conceived to exist in magnitudes regarded as modi- 
fications of space may also be pei^ceived to exist in 
similar magnitudes regarded as portions of bodies. The 
perfect straight line and the perfect triangle and the 
perfect circle are not merely imaginable forms, but 
tangible substances. But it is further assumed by the 
author, that the sensible properties of bodies, whose very 
existence can only be proved by the testimony of expe- 
rience, may exist, along with the Geometrical qualities, in 
a manner in which experience has never presented them. 
Thus " figures of all kinds, lines and points," are "always 
considered as exhibited on a hard body of some kind, 
which causes the position of the several parts or points 
to be fixed with relation to one another; and will, on 
occasion, be supposed to be turned about an assigned 
point or points, in any manner that can be shown to be 
practicable with the hard body on which they are under- 
stood to be represented. Nevertheless, the application 
of one object to another will, when required, be imagined 
to take place without bar of corporeal substance ; — that 
is to say, without impediment from the existence of 
other parts than those it is desired to compare." In 
other words, the surface of a solid and the linear boundary 
of a surface may be considered ad libitum as in or out 
of connection with the bodies of which they form part, 
retaining in both cases the attributes of body, such as 



262 APPENDIX. 

hardness. Surely such assumptions as these, be they 
legitimate or illegitimate, are to be treated as postulates 
or axioms. At any rate they are not definitions. 

But further: a Body is defined to be "any thing that 
can be made the object of touch ;" and a hard body is 
" a body which resists all change of form." But bodies 
which resist all change of form are assumed at the same 
time not to resist all change of size ; for the genesis of 
the straight line and the proof of the axiom of parallels 
are made to depend on a supposed inflation of the 
sphere. Here is another implied postulate or axiom. 
" A hard body may be increased or diminished in size 
without losing its hardness." Empirically, this is untrue. 
A body which resists all change of form can never in 
practice be expanded or contracted ad libitum. To 
assume it as imaginably true is to assume an axiom, not 
a definition. 

Again : the author attempts to prove the majority of 
the axioms of Euclid by superposition ; laying down 
beforehand these two definitions; " Things which occupy 
the same place, are said to coincide;" and, "Magnitudes 
which, if their boundaries were applied to one another, 
would coincide, or might be made capable of doing so 
by a different arrangement of parts, are called equal.'* 
In the latter definition again there is an assumed postu- 
late : " The parts of a body may be arranged in any way, 
without affecting the magnitude of the body." Otherwise 
the two meanings of the term equal are a mere equi- 
vocation; and the demonstration of the equality of any 
two given bodies is a mere play upon words. A is equal 
to B because it actually coincides with it. C is equal to 
B because it may be made to coincide with it. But how 
do 1 know that it is the same C before and after the 
change in the arrangement of its parts ? If I may^ssert 
that the two bodies are notv equal, because a different 



APPENDIX. 263 

arrangement of parts may make them so, why may I not 
assert that they are now equal, because by taking away a 
part of one of them they may become so ? 

But even after this assumption is made, it may be 
questioned whether the principle of superposition can 
be legitimately applied to magnitudes considered as 
exhibited on a hard body. Magnitudes in space can be 
constructed a priori in a pure intuition, and in any one 
part of space, as readily as in any other. Hence they 
may be transported by the same intuition from one 
position in space to another, and all their constituent 
attributes with them ; for they contain no attribute 
which is not presented in the image. But the empirical 
qualities of a hard body cannot be constructed a priori 
in a pure intuition; and tangibility, which the author 
adopts as the test of corporeity, cannot be conveyed into 
the mental image by the construction, nor conceived to 
exist, so long as it is transferred from one place to 
another solely by the imagination. If I draw two 
triangles upon paper, I can only shew their coincidence 
as bodies by cutting one out and placing it on the other. 
Thus the statements of Geometry are reduced to empirical 
truths dependent on actual measurement; a method quite 
as applicable to theorems as to axioms, and which, con- 
sistently carried out, would dispense with demonstration 
altogether. For if I may prove by measurement that 
magnitudes which are equal to the same are equal to 
each other, I may apply the same test with equal direct- 
ness to shew that the angles of a triangle are equal to 
two right angles. 

On the whole then, notwithstanding the ingenuity and 
ability of many of the details of Colonel Thompson's 
work, I cannot help thinking that he has failed in his 
attempt to demonstrate a system of Geometry without 
axioms. Such a demonstration, if successful, would be 



•2(i4 



APPENDIX. 



a solvitur ambulando to the entire argument of the present 
note. But no such attempt has as yet succeeded ; and 
on logical grounds I think it may be made abundantly 
manifest that none ever can succeed. 

As an appropriate conclusion to this note, 1 subjoin a 
specimen of Euclid reduced to syllogisms, extracted 
from the very curious and rare Analyses Geometries of 
Herlinus and Dasypodius. I have selected the fifth 
proposition of the first book, as that which has also been 
analysed by Mr. MilP. To the curious in such subjects 
it may be interesting to compare the two demonstrations. 

PjlOPOSITIO V. 

Theorema. 

Tmv l(TO(rx.s\cov rgiyoovoov u\ Trgos tj5 /Sacrg/ yooviui 'l(roti otWriKuis 
glo"/* KOLi Trqoorsyi^Kfi^BKTm rcov 'icrwv euSsiwv, at mo t^v ^olg'iv 
yu^vioLi 'i(Ta.i otWYjXone; 'k(TOVTcn. 

Triangulorum qui duo sequalia habent latera, anguli 
ad basin sunt aequales. Et productis aequalibus illis 
rectis, etiam qui sub basi sunt anguli, inter se erunt 
aequales. 

Sit triangulus aequicrurus a/3y, habens latus a/3 aequale 
lateri ay, et ducantur lineis 
a/3, ay, Itt^ £uQslix$ linesB /35, ys. 6 . 
Sio^to-jxoV. Dico quod angulus 
a/3y est aequalis angulo ay/3. 
Et quod angulus y/35 est 
gequaiis angulo /3ys. ^ xaro- 
G-KeuYj. Sumatur in linea /35 
punctum quodvis ^. Tolla- 
tur a majore linea ae, minori 
a^ aequalis linea uyj, per pro- 
positionem tertiam. Ducan- 
tur rectse ^y, >?/3. 

^ Logic, b. ii. chap. iv. 




APPENDIX. 265 

Syllogismi quatuor. 

Primus. Quicunque duo trianguli habent duo latera 
duobus lateribus aequalia, alterum alteri, et angulum 
angulo aequalem, qui gequalibus lineis continetur, etiam 
basin basihabebunt sequalem, et reliquos angulos reliquis 
angulis sequales, alterum alteri, quos aequalia latera sub- 
tendunt. Trianguli /3a»j, ya? habent duo latera /3a, aij, 
aequalia duobus lateribus ya, a?, alterum alteri, latus /3a 
lateri ya, et latus a>j lateri a?. Et habent angulum /3a)j 
communera. Ergo. Trianguli j3a>j, yoii!^, habent basin /3>j 
aequalem basi y^, et angulum a/3>j aequalem angulo uy}^, et 
angulum a>j/3 aequalem angulo u^y. Explicatio. Major 
est propositio quarta. Minoris pars prima est uttoSso-is. 
Secunda est nota Ix tv)? xaracxeu^f. Tertia est nota per 
se. Secundus. Si ab aequalibus tollantur aequalia, quae 
relinquuntur sunt aequalia. A lineis aequalibus a?, «>j, tolle 
lineas aequales a/3, uy. Ergo. Manet recta /3?, aequalis 
rectae y)j. Explicatio. Major est xoiv^ hvoiu. Minoris 
pars prior est nota ?x t>5? xarao-xsy^j. Posterior est i>7r6$s(ng. 
Tertius. Quicunque duo trianguli habent &c. ut syllog. 
pri. Trianguli /3>3y, y?/3, habent duo latera ^>j, r^y, aequalia 
duobus lateribus y?, ^/3, alterum alteri, latus /3>) lateri y?, 
et latus r\y lateri ?i3, et habent angulum /S>3y aequalem 
angulo y?/3. Ergo. Trianguli /Srjy, y?6, habent angulum 
/3y)j aequalem angulo y/3^, et angulum y/3)j aequalem angulo 
/3y?. Explicatio. Major est propositio quarta. Minoris 
pars prima et tertia est conclusio syllog. primi. Secunda 
est conclusio syll. secundi. Quartus. Si ab aequalibus 
tollantur aequalia, quae relinquuntur sunt aequalia. Ab 
aequalibus angulis aj8»), uy}^, tolle aequales angulos y/3>j, 
/3y^. Ergo. Manet angulus a/3y, aequalis angulo ay/3. 
Explicatio. Major est xo»v^ twoiu. Minoris pars prior 
est conclusio syll. primi. Posterior est conclusio syll. 



266 APPENDIX. 



tertii. to o-uf^Trg^ao-jtAa. Ex conclusione syll. quarti liquet 
trianguli a/3y, angulos a/3y, ay/3, qui sunt ad basin esse 
aequales. Et ex conclusione syll. tertii liquet angulos 
/3yr}, y^5, qui sunt sub basi esse aequales. Triangulorum 
igitur qui duo habent sequalia latera, &c. oirsg shi hl^ai. 



appendix. 267 

Note M. 
on the classification of fallacies. 

It has been before observed % that Aristotle's Treatise 
TTsg) ao^KTTiKwv iKkyyjfiv has properly only a historical 
value ; that it is important as an account of modes of 
reasoning in use at the period to which it refers; but 
that it is not, and does not profess to be, a classification 
based on any logical principle. Its divisions, however, 
have been followed without question by the majority 
of subsequent logicians, centuries after the circumstances 
which gave it its chief value had ceased to exist; and 
its language has become in a manner classical, though 
not always restricted to the sense originally intended 
by its author. Petitlo Principii and Ignoratio Elenchi 
still hold their place as recognised forms of fallacy; 
and the continued use of the Aristotelian nomenclature, 
at different times and under different circumstances, has 
given in some respects a permanent value to that which 
originally was designed only for a temporary purpose. 
It is not therefore intended in the present note to pro- 
pose an entirely different classification and nomenclature, 
but only to point out certain principles, according to 
which, if Logic is regarded as the Science of the Laws 
of Thought, an arrangement of Fallacies may be at- 
tempted on properly logical grounds, and some of the 
deficiencies of the received enumeration supplied. 

The Aristotelian list is confined to Fallacies connected 
with Reasoning. But if Logic is the Science, not of the 
Laws of Reasoning only, but of those of Thought in gene- 
ral, it will follow that the spurious forms of Conception and 
Judgment are equally entitled to a place among Logical 
Fallacies. And if all the processes of Thought, so far 

» See above, p. 129, note a. 



268 APPENDIX. 

as they come within the province of Logic, are governed 
by the same laws, we may naturally expect to find some 
resemblance between the illegitimate forms of each. 
The resemblance, as will be seen hereafter, is by no 
means perfect; but the same general principles of classi- 
fication will be found applicable to the various processes 
of Thought, whether we are examining their legitimate 
or their illegitimate results. 

The first and most obvious principle of division is 
into Formal and Material Fallacies, according as the 
source of the deception lies in the act of thought itself, 
or in the object upon which, or the circumstances 
under which, it is exercised. Strictly speaking, Formal 
Fallacies alone come under the cognisance of the Logica 
docens, or Logic properly so called; as being apparent 
but not real thoughts, or at least not the kind of thoughts 
which they profess to be. Material Fallacies, where 
the thought is legitimate, but the relation to things 
inaccurate, belong properly to the province of the Logica 
utens, and can only be adequately guarded against by 
that branch of knowledge which takes cognisance of 
the things. A minute division of Material Fallacies 
may thus be carried on to an indefinite extent ; for any 
object about which we think may be represented in 
thought inaccurately or untruly. The Logician must 
content himself with indicating the most general prin- 
ciples of such a division; and that not strictly as a 
portion of the theory of his science, but as a hint for 
its application to practice. To these two classes of 
Fallacies, which are those which suggest themselves 
a priori, as implied in the idea of any possible exercise 
of thought, it becomes necessary in practice to add a 
third class, comprising those which arise from the 
ambiguities of language. Words, whether written, or^ 
spoken, or exhibited in some other system of signs, are 



APPENDIX. 209 

proved by experience to be universally necessary in 
practice, both to the formation and to the communication 
of thought; and any defect in this indispensable instru- 
ment is communicated to the operations which it per- 
forms. This was clearly seen by Aristotle and his 
followers, who have assigned a prominent, indeed too 
prominent, a place to language in their classification, by 
dividing Fallacies, in the first instance, into those in 
dictione and those extra dictionem; according as the de- 
ception does or does not depend upon the particular words 
in which the reasoning is conveyed^. Looking to the 
actual position of language in relation to thought, it will 
be better to adopt a threefold division of Fallacies; those 
in the Thought, those in the Matter, and those in the 
Language ; the last corresponding to the fallacice in dic- 
tione of Aristotle; the two former representing a still more 
important though often neglected distinction, which is 
lost sight of in the vague negation of extra dictionem. 

In the application of this principle of division to the 
several operations of Thought, as exhibited in the follow- 
ing Table, some slight differences will present themselves, 
which in some instances will explain themselves, while 
in others a few preliminary words of explanation may 
be desirable. Fallacies of Language, it is obvious, will 
become more numerous as the process of thought be- 
comes more complicated. While a concept can be 
misapprehended only in the term (whether expressed by 
one word or more) in which it is conveyed, a Judgment 
may be ambiguous, either in the meaning of one of its 
terms, or in its entire construction ; and a Reasoning 
admits of still further ambiguity, from the repetition of a 
term or sentence in different senses. Hence a different 
enumeration of Fallacies in dictione will be required in 
different parts of the Table. 

*» For some further remarks on this division, see p. 131, note b. 



270 APPENDIX. 

As regards Formal or Logical Fallacies, a fuller ex- 
planation may be needed. The ultimate test of the 
logical validity of any thought is conceivahility. This 
test may be applied to judgments and reasonings, as 
well as to concepts. A concept is logically real if it is 
conceivable; that is to say, if its constituent parts can be 
combined with each other in an unity of representation. 
If it complies with this criterion, it is real as a thought : 
whether its supposed object be real as a thing, is a 
question with which Logic has no concern. A judgment, 
again, is logically true or necessary, (for Logic recognises 
no truth short of necessity,) if its contradictory is incon- 
ceivable : it is logically false or impossible, if it is itself 
inconceivable; but if two contradictory assertions are 
both equally conceivable, it does not lie within the pro- 
vince of Logic to determine their truth or falsehood. A 
reasoning, in like manner, is logically necessary, if the 
contradictory of the conclusion cannot be conceived as 
true, consistently with the assumed truth of the premises : 
it is logically impossible, if the conclusion itself cannot 
be so conceived. If, however, the conclusion and its 
contradictory are equally conceivable along with the 
assumed truth of the premises, the conclusion may or 
may not have a material value, but it is one which cannot 
be recognised by Logic. 

But though the test of conceivahility is thus applicable 
to judgments and reasonings, as well as to concepts, it is 
applicable in a different manner. A given combination 
of attributes may be inconceivable, either because it 
contains too little, or because it contains too much. 
That is to say, it may either be defective in the con- 
ditions under which alone attributes can be united in 
representation, or it may contain such attributes as 
mutually exclude one another. Thus, inasmuch as unity 
of representation is only possible under the condition 



APPENDIX. 271 

of limitation by difference, because the thing repre- 
sented must be known as an actual object, and not as 
the universe of all possible objects, it follows that the 
indefinite ideas corresponding to the terms Thing, Ex- 
istence, Being in general, are not conceivable, as having 
no distinctive characteristic. They may be elements of the 
conceivable; that is to say, they may become conceivable 
when combined with and determined by other attributes; 
but so long as they are given as isolated, and therefore 
as unconditioned, they are inconceivable. The logical 
rule here violated is the Law of Identity, which requires 
that every object should be conceived as itself, and as 
distinguished from every thing else. Here the supposed 
Concept contains too little. On the other hand, if the 
given attributes are incompatible with each other, the 
rule violated is the Law of Contradiction, which requires 
that two contradictory attributes should not be united in 
the same object. Here the supposed Concept contains 
too much. The third law of thought, that of Excluded 
Middle, may also be violated in relation to the same 
process, if we attempt to conceive an object of which 
neither of two contradictory attributes is predicable. 
Here again, the supposed Concept contains too little. 

But it is obvious that these three laws cannot all be 
equally violated in a pretended act of Judgment or of 
Reasoning. In Judgment, the concepts are already given ; 
and nothing remains to be done, but to connect them 
together by an affirmative or negative copula. Here 
there is no room for a deficiency of attributes; which 
would affect the conceivability of the terms themselves, 
not the possibility of their union in a judgment. The 
only logical fallacy possible must consist in uniting 
notions which are essentially distinct, or in separating 
such as are essentially the same. In Reasoning, again, 
the truth of the premises and the conceivability of the 



272 APPENDIX. 

terms, are not examined, but assumed; and the only pos- 
sible logical fault must consist in drawing a conclusion 
incompatible with the premises themselves, or with some- 
thing which they imply. In these two cases, the only 
possible instances of inconceivability must arise from 
a direct or indirect Contradiction. 

A Fallacy, according to Aristotle, is a reasoning which, 
either in matter or form or both, appears to be that 
which it is not^. Extending this definition from the 
process of reasoning to that of thought in general, we 
may regard any thought as fallacious, which, in form or 
matter, has an apparent but not a real validity ; and a 
Logical or Formal Fallacy is one which exhibits an ap- 
parent but not a real conformity to the Laws of Thought. 
An apparent thought may thus be formally fallacious in 
two ways ; either generally, because it is not a thought 
at all ; or specially, because it is not the kind of thought 
which it professes to be. For the elements of a judg- 
ment may be perfectly legitimate as objects of con- 
ception, but self-destructive when united together as 
parts of a judgment; and the premises and conclusion 
of a syllogism may be valid, even all together, as in- 
dependent judgments, yet involve a concealed contra- 
diction when placed in the relation of antecedents and 
consequent in an act of reasoning. Thus, if it be argued 
"All A is B, C is not A, therefore C is not B," it is 
obvious that the three statements, viewed merely as judg- 
ments, may be all true together. But when we view them 
as parts of a syllogism, we assert that C is not B, because 
it is not A; in other words, that nothing can be B which is 
not A, or that every B must be A. Whereas the premise, 
in stating that all A is B, leaves it open as at least a pos- 

c Topics i. 1. 3. 'EpiffTiKhs S' iarl (rvWoyi(riJ.hs 6 e/c (paivofidvwv ivSo^p, 
fjL^ &vTOi)v 54, Koi 6 e| iuSS^ciJU f) (paLvofxivwv 4v56^wv cpaivSfxepos. See also 
So}>h. Elench. c. 2. 



APPENDIX. 273 

sible truth that some B is not A. Hence the same 
belief is regarded as possible and impossible at the 
same time ; and thus the conclusion, though not directly 
at variance with what the premise asserts, cannot be 
drawn consistently with what it permits. Hence these 
and cognate forms of reasoning are classed in the Table 
as violating the Law of Contradiction indirectly; and the 
conclusion is noted as formally invalid, though mate- 
rially it may be either true or false. Thus the whole 
process may be valid as a series of judgments, but not 
as a reasoning ; and the thought, therefore, is not the kind 
of thought which it professes to be. On the other hand, 
if a conclusion is drawn opposed to that which the laws 
of thought require, the conclusion is neither materially 
nor formally possible ; and the supposed reasoning is in 
reality no thought at all. Thus we may, verbally at least, 
argue, " All A is B, C is A, therefore C is not B ;" which 
requires- us to conceive C as being at the same time B 
and not B. Here the Law of Contradiction is violated 
directly. The relation of logical fallacies to this law 
will be seen much more clearly, if, in accordance with 
the system of Sir William Hamilton, we assign to the 
predicate as well as to the subject of every proposition 
an expressed mark of quantity. 

To attempt a complete enumeration of Material 
Fallacies would be an endless as well as a profitless 
task. Under the head of Reasoning, it has been thought 
sufficient to arrange in their proper places the members 
of the usually received list. The arrangement has been 
made according to the instances given by Aldrich and 
other modern Logicians, as being most familiar to the 
majority of readers. These, however, occasionally differ 
in points of detail from those which are found in the 
original text of Aristotle. The discrepancy is of little 
consequence ; as the notes to the corresponding portion 

T 



274 APPENDIX. 

of Aldrich's text will in most instances enable the reader 
to compare and classify Aristotle's examples for himself. 
Indeed, Aristotle himself confesses that the arrangement 
is in some degree arbitrary, and that the same Fallacy 
will admit of being classed under different heads. 

As regards Material Fallacies of Conception and Judg- 
ment, I have contented myself with indicating, in the most 
general way, the sources of Obscurity and Indistinctness 
in Concepts, and of Falsity in Judgments. A concept is 
obscure, when it cannot be distinguished as a whole from 
certain others : it is indistinct, when its several com- 
ponent parts cannot be distinguished from each other^. 
The obscurity or indistinctness of a concept may ob- 
viously arise, either from accidental circumstances, such 
as the want of a sufficient observation of the object on 
the part of this or that individual thinker, or from 
circumstances essential to the concept itself, such as the 
want of those conditions which experience shews us to 
be indispensable to all clear or distinct thinking. Under 
this head may be classed the notions, so familiar to all 
students of Logic, of summum genus and injlma species. 
Both of these terms represent limits to which we may 
indefinitely approximate in thought, but which we never 
actually attain. Neither of them can be regarded as 
logically inconceivable ; for, under different conditions 
of the matter of our thought, both might be practically 
apprehended. But, in actual thinking, it becomes manifest 
that our several concepts present in all cases such an 
affinity or continuity one with another, that it is im- 
possible, on the one hand, to fix on two cognate genera 
which possess no common element to form a higher 
genus, (until we arrive at abstractions too empty to be 



d This distinction is due to Leibnitz. See his Meditationes de CognitionCf 
Veritate et Ideis. Opera, ed. Erdmann, p. 79. 



APPENDIX. 275 

conceived at all,) or, on the other hand, to arrest the 
process of subdivision at any limited number of at- 
tributes, as the greatest number that can possibly be 
united in one concept^. 

Thus the notion of a logical highest genus, that is, 
of a concept so simple as to be incapable of further 
analysis, is essentially obscure ; for, in actual thought, 
we find that, so long as there is limitation and difference, 
there is also community, and, therefore, a possibility 
of further analysis f. Again, the notion of a logical lowest 



e The Highest Genus and Lowest Species of Logic must not be con- 
founded Avith the same terms as applicable to this or that branch of 
natural science. The Highest Genus in any special science is the general 
class, comprehending all the objects whose properties that science in- 
vestigates : the different Lowest Species are the classes at which that 
special investigation terminates. In Geometry, for example, under the 
sKmmum genus of magnitudes in space, we find these coordinate injimce species 
of triangles, the equilateral, the isosceles, and the scalene. The Geo- 
metrical properties of the figures are not affected by further subdivision. 
But the Logician, as such, knows nothing of Geometrical Imiitations. To 
him the highest genus and lowest species are limits of the possibility of 
thought ; the former denoting a notion so simple as to admit of no further 
subtraction, the latter^ a notion so complex as to admit of no further 
addition. In thought, the notion of an equilateral triangle whose sides 
are three feet long is a subordinate species to that of an equilateral triangle 
in general. 

f It is not easy to draw the line between the materially and the formally 
inconceivable. Being in general (^ns), and such like abstractions, may 
be regarded as formally inconceivable, as having no contents. But these 
abstractions are not necessarily identical with the notion of a highest 
genus ; — indeed, the majority of Logicians have placed the summa genera 
in the Categories, of which Ens and the other transcendents were regarded 
as predicable equivocally, or analogously, but not univocally. But the 
Categories, again, are practically inconceivable perse; for a substance is 
only known by its attribiTtes, and an attribute as existing in a substance. 
But it is at least supposable that, under other conditions of experience, 
we might arrive at notions suflSciently definite to be conceivable, yet so 
diverse as not to admit of classification under a higher genus ; and this is 
virtually admitted by Kant, who, notwithstanding, regards the laws of 
homogeneity, specification, and continuity as logical principles of the 
reason. I prefer to consider them as empirical, though perhaps indicating 
psychological conditions of experience. Thus viewed, they are not, properly 



276 APPENDIX. 

species, or a combination of all conceivable compatible 
attributes, is essentially indistinct; for the number of 
such attributes is indefinite, and, to go through them 
in thought, enumerating and distinguishing one from 
another, would require an infinite grasp of mind, and ah 
infinite length of time, for its accomplishment. 

Another class of notions may be specified as materially 
inconceivable ; those, namely, which, though presenting 
no logical contradiction, contain attributes materially 
heterogeneous, and thus incompatible with each other. 
Such combinations of attributes as circular virtue, or 
coloured thought, are of this character. "Black spirits 
and white, red spirits and grey," are only con- 
ceivable by investing the spirits with a body for the 
occasion, and not by connecting the idea of colour with 
that of spirituality. To the same class belong all com- 
binations of attributes inconsistent with the a priori 
conditions of intuition; such as a bilinear figure; which, 
though not logically contradictory, are mathematically 
inconceivable. These must be carefully distinguished 
from those notions which, though empirically known to 
be unreal, are yet perfectly consistent as thoughts; such as 
the conception of a centaur, or of a golden mountain. In 
respect of these last. Logic recognises no distinction 
between the real and the unreal. An opposite class of 
notions materially inconceivable, are those which are 
defective, as separating attributes whose union is testified 
by experience to be indispensable to conception. Thus, 
inasmuch as we know by experience, that no surface can 
be conceived, without being of some colour, and that no 
colour can be conceived, except on some surface, the 
conceptions of an uncoloured surface or an unextended 
colour, though they present no logical contradiction, 

speaking, laws of thought ; and thus, as far as Logic is concerned, they 
belong to the matter of thought, not to the form. 



APPENDIX. 277 

must be classed as essentially, though materially, incon- 
ceivable^. 

As regards the truth or falsehood of Judgments, Logic 
properly takes cognisance of Formal Truth or Falsehood 
only, which depends on the agreement or disagreement 
of a thought with its own laws. Material Truth, which 
is sometimes defined as consisting in the agreement of 
the thought with its object, might be more correctly 
explained as consisting in the agreement of the object 
as represented in thought with the object as presented 
in intuition ; for the object exists, relatively to us, 
only as given in some form of intuition. But, however 
it may be defined, it is manifest that no general law 
or criterion of material truth and falsehood can be 
given ; for the essence of such truth consists in its 
adapting itself in every case to the diversities of this or 
that special presentation''. To enumerate in detail all 
the various sources of material falsehood would be 
impossible ; I have contented myself with referring to 
the three general heads of Mathematical, Metaphysical, 
and Physical Judgments; which appear to possess essen- 
tially different degrees of certain t}^ or impossibility. 
These propositions will admit of a different classification, 
according to the theories held by different writers as to 
their origin. By some, mathematical judgments will be 
classed with physical, as due solely to experience : by 
others, they will be merged in logical truth or falsehood, 
as owing their evidence to laws of thought. Metaphysical 
judgments, again, will be considered by some as purely 
empirical : while by others they will be referred to 



s The error of those philosophers who maintain that colour can be 
conceived without extension is exposed by Sir W. Hamilton, Reid's Works, 
p. 143. 

h That a general criterion of material truth is not only impossible but 
self-contradictory, is shewn by Kant, Logik, Einleitmig, VII. 



278 APPENDIX. 

certain fundamental laws of human belief, originating in 
the constitution of the mind itself. Into the various 
controversies connected with these questions it would be 
irrelevant now to enter. The reasons for the classification 
which I have adopted will be found given at length in a 
separate work, to which for the present I must content 
myself with referring i. 

i See Prolegomena Logica, chap. iv. and v. 



;s. 



Of Reasoning. 



In the Matter. 



Conception given as 

unconditioned. (Law 

of Identity,) e. g. 

Being in general. 



Cc 

S( 

(1 



Bctly. 
tion logi- 

htssible, as 

Directly.iing what 
(by Statem^e permits. 
e.g. a surface '^^^^^^^^ 
white and not aaterially 
ut is not 

Conceptioif^^y-^ 



impq 



Attributes heterogeneous. 

e. g. circular virtue, 

or bilinear figure. 



Undistributed 
Middle. 



In the Language. 
(Fallaciee in Dictione.) 



Of a Term. 
I 



In itself. In its relation. 
(iEquivocatio, (Compositio, 
Accentus, Divisio.) 

Figura 
Dictionis.) 



Of a Propo- 
sition. 
(Amphibolia.) 



j false , 
jding 
sa pro 



Premise doubtful. 

(including 
Fetitio Principii.) 



Conclusion irrelevant. 
(Ignoratio Elenchi.) 



tionum.) 



Judgi 



Directly. 
Contradiction as: 
e. g. black is not 



W'*^ 



In the Language. 
Judgments ambiguous. 



In a single Term. 
(iEquivocatio.) 



In the whole 

Proposition. 

(Amphibolia.) 



278 APPENDIX. 

certain fundamental laws of human belief, originating in 
the constitution of the mind itself. Into the various 
controversies connected with these questions it would be 
irrelevant now to enter. The reasons for the classification 
which I have adopted will be found given at length in a 
separate work, to which for the present I must content 
myself with referring i. 

* See Prolegomena Logica, chap. iv. and v. 






H 



TABLE OF FORMAL AND MATERIAL FALLACIES. 



FALLACIES 



Of Conceptit 



Of Judgment. 



In the Matter. 



Conception given as Conception given a; 
unconditioned. (Law self- contradictory. 



of Identity,) e. g. 
Being in general. 



(Law of Contradii 



Conception given as 
formally defective. 
(Law of Excluded 

Middle) e. g. a sur- 
face neither white 
nor not white. 



Directly. Indirectly. 

(by Statement) (by Inference) 

e.g. a surface both e.g. a surface both 

white and not white. white and black. 



Conceptions materially 
impossible. 



In the Language, 
where a single term 
admits of more than 



Attributes heterogeneous, 
e, g, circular virtue, 
or bilinear figure. 



Matter defective. As a whole. 

e. g. an uncoloured surface. (Obscure.) 



Conceptions materially 
incomplete. 



In the pai-ts. 
(Indistmct.) 
1 



Essentially. Accidentally. Essentially. Accidentally, 

(summum genus.) (from imperfect (infima species.) (from want of 
observation.) analysis.) 



Of Reasoning. 



In the Form. 

(Fallacia Consequentls) 

conclusion implies 

a contradiction of 

a premise. 



In the Matter. 



Directly. 
Conclusion logically 
impossible, as contra- 
dicting what the 
premise asserts. 
(This consequence 
can be neither for- 
mally nor materially 
valid.) 



Indirectly. 
Contradiction logi- 
cally inadmissible, as 
contradicting what 
the premise permits. 
(This consequence 
may be materially 
valid, but is not 
formally.) 



Illicit Process 
of Major. 



Of a Term. 

In itself. In its relation, 
(.ffiquivocatio, (Compositio, 



In the Language. 
(Fallaciffi in Dictione.) 



Of a Propo- 
sition. 
(Amphibolia.) 



Accentus, 

Figura 
Dictionis.) 



Divisio.) 



Term imperfectly 

conceived. 

(Accidens, 

A dicto 

secundum quid.) 



Premise false . 

(including 

Non causa pro 

causa, 

Plurium 

Interrogationum.) 



Premise doubtfiil. Conclusion irrelevant, 
(including (Ignoratio Elenchi.) 

Petitio Principii.) 



In the Form. 
Judgments logically false. 



Directly. 
Contradiction asserted, 



In the Matter. 
Judgments materially false. 



In the Language. 
Judgments ambiguous, 



Indirectly. 
Contradiction implied, 
g. black is not black. e. g. black is white. 



At variance with At variance with 

a priori intuition. empirical intuition. 

(Mathematically false.) (Physically false.) 



At variance with 
the conditions of 

personal consciousness. 

(Metaphysically false.) 



In a single Term. 
(,^quivocatio.) 



In the whole 
Proposition. 
(Amphibolia.) 



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